LB 


Variable  Factors  in  the  Binet  Tests 


A  DISSERTATION 

presented  to  the 

Faculty  of  Princeton  University 

IN  Candidacy  for  the  Degree 

OF  Doctor  of  Philosophy 

BY 

CARL  C.  BRIGHAM 


Princeton 

Princeton  University  Press 

1917 


Variable  Factors  in  the  Binet  Tests 


A  DISSERTATION 

presented  to  the 

Faculty  of  Princeton  University 

IN  Candidacy  for  the  Degree 

OF  Doctor  of  Philosophy 

BY 

CARL  C.  BRIGHAM 


Princeton 

Princeton  University  Press 

1917 


VARIABLE  FACTORS  IN  THE  BINET  TESTS 

Table  of  Contents 

I.     Introduction   i 

II.     Subjects  and  Methods 8 

III.     The  Personal  Equation i8 

VI.     Grade  Correlations 37 

V.     Sex  Differences  65 

VI.     Summary 91 


I.    INTRODUCTION 

During  the  past  decade,  the  Binet-Simon  measuring  scale  for 
intelligence  has  received  considerable  attention,  and  a  large 
amount  of  literature  has  appeared  on  the  subject.  No  attempt 
has  been  made  in  the  following  pages  to  review  all  the  literature 
on  this  scale  or  other  systems  of  intelligence  testing.  Kite  (38) 
gives  an  excellent  account  of  the  history  and  nature  of  the  scale. 
Kohs  (41)  has  assembled  a  very  complete  bibliography  on  the 
subject  up  to  June  1914.  Schmitt  (57)  gives  an  historical  ac- 
count of  the  development  of  the  various  attempts  to  correlate 
psychological  findings  with  general  intelligence,  particularly  in 
this  country  and  England.  Bo'bertag  (10)  and  Schmitt  both 
give  detailed  descriptions  and  analyses  of  the  individual  tests. 
Stern  (62)  has  devoted  a  monograph  to  the  collection,  exposition 
and  critical  analysis  of  the  large  amount  of  data  bearing  on  the 
problem  of  intelligence  testing,  and  in  another  work  (61)  has 
assembled  the  literature  of  cognate  fields.  The  literature  bearing 
on  the  Binet  scale  up  to  19 12  is  largely  descriptive  of  the  scale 
itself,  the  standard  methods  of  procedure,  etc.  The  more  recent 
literature  has  been  critical  and  reveals  a  tendency  at  the  present 
time  for  investigators  to  depart  from  the  methods  of  the  exten- 
sive application  of  the  scale  as  a  whole  to  the  more  intensive 
study  of  the  individual  tests. 

All  systems  of  intelligence  tests  may  be  classified  as  qualitative 
or  quantitative.  The  qualitative  system  consists  of  an  aggrega- 
tion of  tests  designed  to  detect  the  capacities  or  incapacities  of 
the  subject  in  order  to  afford  the  experimenter  an  opportunity 
to  make  a  diagnosis  concerning  the  subject's  mentality.  This 
method  throws  the  responsibility  for  the  final  diagnosis  on  the 
experimenter.  The  system  of  tests  proposed  by  Healy  and  Fer- 
nald  (34)  are  of  this  type.  Quantitative  systems  of  tests  necessi- 
tate a  final  score  of  some  sort,  whether  that  score  be  in  the  form 
of  a  mental  age,  a  mental  quotient,  a  certain  number  of  points, 


2  CARL  C.  BRIGHAM 

a  coefficient  of  intellectual  ability,  a  percentile  rank  or  what  not. 
The  essential  characteristics  of  the  quantitative  systems  are  the 
interpretation  of  the  total  scores  in  terms  of  the  age  of  the  sub- 
ject, and  the  placing  of  the  responsibility  for  the  final  diagnosis 
on  the  tests  rather  than  the  experimenter, 

Binet  and  Simon's  1905  scale  (5  and  6)  was  of  the  qualitative 
type.  A  series  of  30  tests  of  approximately  increasing  difficulty 
was  published  with  directions  for  their  application.  The  authors 
reported  in  a  general  way  that  from  their  experience  in  examin- 
ing a  few  selected  normal  children  of  different  ages,  and  other 
subnormal  children  in  the  schools  and  at  the  Salpetriere,  approxi- 
mate levels  of  performance  could  be  found  characteristic  of  the 
development  of  normal  children  of  3,  7,  9  and  11  years  chrono- 
logically, the  performance  of  idiots,  imbeciles  and  morons  cor- 
responding roughly  with  that  of  normal  children  of  3,  7  and  9. 
Although  the  reference  to  chronological  ages  introduced  the 
quantitative  element,  at  no  place  were  the  authors  insistent  on 
this  point,  merely  stating  that  they  had  found  the  series  of  tests 
exceedingly  valuable  in  diagnosing  and  classifying  defectives, 
and  in  their  opinion  others  would  also  find  it  valuable. 

The  1908  scale  (7)  was  quantitative  in  character  owing  to 
the  introduction  of  the  concept  of  "mental  age".  It  included 
a  list  of  56  tests  grouped  according  to  ages  from  3  to  13,  each 
group  containing  from  four  to  eight  tests.  Most  of  the  tests  of 
the  1905  series  were  included,  the  additions  including  in  a  large 
measure  tests  of  a  scholastic  nature.  The  authors  gave  directions 
for  applying  the  series  and  for  computing  the  resultant  "mental 
age".  A  child  testing  three  years  below  his  chronological  age 
was  to  be  considered  defective. 

Although  the  scheme  of  the  1908  series  was  entirely  quantita- 
tive, the  authors  did  not  discard  the  qualitative  idea,  and  they 
cautioned  against  the  application  of  the  scale  in  the  manner  of 
a  measure  of  height  or  weight.  The  border  line  between  the 
idiot  and  the  imbecile  was  fixed  by  the  ability  to  use  and  compre- 
hend spoken  language.  The  imbecile  was  differentiated  from 
the  moron  by  the  use  of  written  language,  illiteracy  being  di^ 


I 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  3 

ferentiated  from  imbecility  by  certain  tests.  The  authors  stated 
that  the  moron  could  be  defined  only  in  terms  of  the  environ- 
ment in  which  he  lived,  and  they  considered  six  tests  important 
in  differentiating  the  moron  from  the  normal  individual  of  the 
Paris  population.  Any  system  of  tests  which  throws  more 
weight  on  some  tests  than  on  others  in  making  a  differential 
diagnosis  is  fundamentally  qualitative  in  kind,  for  the  responsi- 
bility is  placed  not  on  the  score  but  on  the  judgment  of  the  ex- 
perimenter. The  idea  of  a  quantitative  measuring  scale  of 
intelligence  however  met  with  instant  favor.  The  interest  that 
actuated  the  psychologists  of  the  "early  nineties"  to  correlate 
the  measurements  of  reaction  time,  motor  ability,  sensory  dis- 
crimination, etc.  with  intelligence  was  revived.  The  scale  was 
translated  into  several  languages  and  applied  to  individuals  of 
many  classes  and  types. 

In  191 1,  the  authors  published  a  revised  scale  (8)  in  which 
many  of  the  tests  of  scholastic  ability  were  discarded,  and  the 
remaining  tests  shifted  about  so  that  there  were  five  tests  for 
every  year  except  one  from  III  to  X  with  similar  groups  for 
"twelve  year",  "fifteen  year"  and  "adult"  mentality.  In  the  same 
year,  Binet  published  an  article  (4),  his  last  word  on  the  sub- 
ject, in  which  he  discussed  many  of  the  criticisms  which  the  scale 
had  received,  and  again  sounded  the  note  of  warning  against 
the  mechanical  interpretation  of  results.  However,  as  one  traces 
Binet's  thought  on  the  subject  through  his  writings,  he  may  see 
the  idea  of  a  qualitative  system  of  tests  gradually  dropping  into 
the  background,  and  more  and  more  weight  placed  on  the  "scien- 
tific" (quantitative)  measure  of  intelligence. 

That  Binet  did  not  depart  entirely  from  the  qualitative  stand- 
point is  shown  by  his  discussion  of  the  test  of  comprehending 
difficult  questions.  "Sometimes  after  an  examination  one  hesi- 
tates on  a  diagnosis.  The  child  has  failed  in  one  or  two  tests, 
but  this  does  not  seem  to  be  convincing.  Failure  to  give  the  day 
and  date  and  the  months  of  the  year  are  excusable  errors,  which 
may  be  caused  by  distraction  or  by  lack  of  education.  But  the 
questions  for  comprehension  dissipate  all  doubts.     We  recall 


4  CARL  C.  BRIGHAM 

several  instances  when  teachers  brought  us  children,  desiring  to 
know  whether  or  not  they  were  abnormal;  occasionally,  in  this 
way  they  set  a  trap  for  us,  but  we  did  not  object,  it  was  fair 
play.  Our  questions  for  comprehension  decided  us  every  time. 
We  remember  one  child  who  was  very  slow  in  answering  as 
though  dull,  his  face  was  expressionless  and  unprepossessing; 
he  knew  neither  the  day  nor  the  date,  nor  what  day  comes  after 
Sunday,  and  he  was  103^  years  old;  his  reading  was  syllabic. 
But  when  we  asked  question  5 :  Why  do  we  judge  a  person  by 
his  acts  rather  than  by  his  words  ?  he  gave  the  following  answer : 
Because  words  are  not  very  sure  and  acts  are  more  sure.  This 
was  enough — our  opinion  was  formed,  that  child  was  not  so  bad 
as  he  seemed."     (Town's  (72)  translation,  page  48.) 

The  popular  interest  that  was  manifest  before  the  advent  of 
the  191 1  scale  was  tremendously  reinforced  in  this  country  by 
Goddard's  (30)  publication  of  the  results  of  the  application  of 
the  scale  to  "two  thousand"  non-selected  school  children  in  Vine- 
land,  N.  J.  Popular  interest  increased  rapidly,  and  the  scale 
continued  to  have  wider  and  wider  application  in  the  hands  of 
less  and  less  experienced  investigators.  The  concept  of  "mental 
age"  was  exceedingly  easy  of  comprehension,  no  apparatus  was 
needed,  and  the  scale  has  now  become  the  common  property  of 
all.  This  development  or  overdevelopment  has  taken  place  in 
spite  of  the  warnings  of  the  authors  themselves  and  the  psycho- 
logical fraternity  in  general.  The  very  fact  of  overdevelopment 
however  is  striking  evidence  that  persons  interested  in  the  social 
sciences  need  a  quantitative  scale  for  measuring  intelligence. 

The  question  whether  the  Binet  scale  is  an  accurate  measure 
of  intelligence  can  be  decided  only  by  the  study  of  the  individual 
tests  and  the  factors  underlying  them.  A  study  of  this  sort  will 
show  the  errors  that  underlie  the  total  score  or  "mental  age", 
and  at  the  same  time  will  show  the  direction  in  which  the  cor- 
rection of  the  scale  should  take  place.  The  proper  understanding 
of  the  individual  tests  involves  the  theory  on  which  the  measur- 
ing scale  was  constructed. 

The  method  which  Binet  and  Simon  used  in  constructing  their 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  5 

measuring  scale  of  intelligence  was  entirely  empirical.  A  large 
number  of  tests  were  given  to  children  of  a  certain  social  status. 
Certain  tests  could  be  shown  to  be  correlated  with  age,  and  in 
the  authors'  opinion  were  correlated  with  intelligence.  The  fact 
that  at  a  certain  age  a  test  could  be  passed  by  a  certain  propor- 
tion of  the  subjects  was  taken  to  mean  that  the  test  in  question 
was  characteristic  of  that  age.  Tests  that  were  characteristic 
of  the  same  age  level  were  then  combined  into  one  age  group. 
In  this  way  a  scale  was  built  up  with  a  number  of  tests  for  each 
age  group.  By  a  certain  arbitrary  system  of  scoring  the  re- 
actions of  a  subject  to  all  or  part  of  the  scale  of  tests,  the  "men- 
tal age"  of  the  subject  was  obtained.  The  comparison  of  the 
"mental  age"  with  the  chronological  age  of  the  subject  would 
show  him  to  be  advanced,  at  age  or  retarded,  and  the  amount 
of  acceleration  or  retardation  would  afford  a  quantitative  index 
of  his  intelligence. 

A  person  could  construct  a  scale  on  the  same  basis  and  arrive 
at  an  age  score  using  entirely  different  tests.  A  scale  could  be 
constructed  containing  tests  of  height,  weight,  vital  capacity, 
strength  of  grip,  circumference  of  the  head,  etc.  and  the  results 
interpreted  in  terms  of  age.  In  this  case  however  the  age  ob- 
tained would  be  more  physical  than  mental.  A  scale  of  tests 
could  also  be  constructed  which  involved  the  subject's  knowledge 
of  geography,  spelling,  history,  grammar,  etc.  but  in  this  case 
the  resulting  age  would  be  determined  very  largely  by  the  amount 
of  training  the  subject  had  received. 

The  assumptions  that  a  child  at  a  certain  age  should  weigh 
25  pounds,  at  another  age  50  pounds,  etc.,  that  a  child  can  repeat 
3  digits  at  one  age,  5  digits  at  another  and  7  digits  at  another, 
and  that  a  certain  percentage  of  children  at  one  age  can  enu- 
merate the  months,  and  a  higher  percentage  at  another  age,  differ 
only  in  the  possible  determiners  to  which  the  growth  may  be  re- 
ferred. In  the  first  case  the  growth  is  referred  to  certain  physio- 
logical processes  which  are  supposedly  independent  of  intelligence 
and  training.  Binet  believed  that  the  principal  determiner  of 
growth  in  the  last  two  cases  was  intelligence,  but  the  possibility 


6  CARL  C.  BRIGHAM 

remains  that  they  might  be  more  or  less  independent  of  intelli- 
gence, and  more  or  less  dependent  on  training  and  other  variable 
factors. 

The  principle  on  which  the  scale  was  constructed  involves  three 
assumptions,  (i)  that  the  individual  tests  are  correlated  with 
age,  (2)  that  the  individual  tests  are  correlated  with  intelligence, 
and  (3)  that  intelligence  is  correlated  with  age — three  distinct 
assumptions  any  one  of  which  does  not  necessarily  involve  the 
others.  The  purpose  of  this  investigation  is  to  study  the  correla- 
tion of  the  individual  tests  with  age,  to  determine  the  variable 
factors  that  might  operate  on  the  tests  to  produce  an  apparent 
correlation  with  age  that  was  not  a  real  correlation,  or  that  might 
alter  the  real  correlation  in  some  way. 

There  is  a  possibility  that  an  error  might  occur  in  the  statistical 
treatment  of  the  results,  so  that  figures  which  would  apparently 
indicate  a  correlation  with  age  of  a  certain  degree  might  actually 
represent  a  correlation  of  another  degree.  Another  variable 
factor  is  the  personal  equation  of  the  experimenter,  who  might 
alter  the  procedure  in  giving  a  certain  test  so  that  the  correlation 
of  that  test  with  age  might  be  different  from  the  correlation 
obtained  by  another  experimenter.  If  the  subjects  of  various 
ages  had  received  different  school  training,  this  difference  might 
introduce  another  factor  which  would  vary  independently  of  the 
age  of  the  subjects.  If  the  tests  used  depended  on  any  inherited 
or  acquired  differences  between  the  sexes,  then  the  correlation 
of  the  tests  with  age  might  be  different  for  the  two  sexes.  If 
any  or  all  of  the  variable  factors  mentioned  prove  to  be  present 
in  the  correlation  of  the  tests  with  age,  then  certain  allowances 
will  have  to  be  made  for  these  factors  in  making  a  diagnosis 
of  the  subject's  intellectual  ability  on  the  basis  of  his  total  score 
or  "mental  age",  and  the  scale  becomes  qualitative  rather  than 
quantitative. 

At  the  Fourth  International  Conference  for  School  Hygiene 
held  in  Buffalo  in  the  summer  of  19 13,  several  persons  of  un- 
questioned authority  in  the  field  of  mental  tests  held  an  informal 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  7 

conference  on  the  Binet-Simon  scale,  reporting  the  results  in 
1914  in  the  form  of  recommendations  and  suggestions  (15). 
The  question,  "How  much  is  the  outcome  of  the  testing  in- 
fluenced by  the  personal  equation,  both  of  the  examiner  and  ex- 
aminee?" was  answered,  "Undoubtedly  there  is  some  influence 
and  it  may  be  a  serious  source  of  error."  Another  question, 
"How  much  do  previous  environment  and  school  training  effect 
the  outcome  of  the  tests?"  was  left  unanswered  by  the  opinion, 
"The  experimental  evidence  thus  far  available  is  conflicting. 
Further  investigation  is  needed."  The  question,  "Should  the 
scale  be  divided,  in  the  upper  years  at  least,  to  furnish  separate 
standards  or  separate  tests  for  the  two  sexes?"  was  answered, 
"We  do  not  know,  and  recommend  this  a  subject  for  investiga- 
tion." The  following  study  is  in  part  an  attempt  to  answer  these 
questions. 

The  method  used  in  this  study  is  that  of  studying  the  indi- 
vidual tests,  disregarding  entirely  the  total  score  or  "mental 
age".  There  are  at  present  so  many  revisions  and  editions  of 
the  Binet  scale,  that  the  term  "mental  age"  has  no  meaning  out- 
side of  the  particular  scale  in  question.  The  tests  that  are  used 
in  the  various  standardizations  are  however  approximately  the 
same,  so  that  conclusions  concerning  the  factors  underlying  the 
individual  tests  have  a  wider  significance  than  those  drawn  from 
the  "mental  ages".  Furthermore  variable  factors  in  the  indi- 
vidual tests  may  balance  each  other  in  the  total  score  so  that 
their  influence  might  be  obscured. 

The  subjects  and  methods  will  be  described  first,  and  in  con- 
nection with  the  methods  of  treating  the  results  a  statistical  error 
will  be  pointed  out.  The  problems  of  the  personal  equation, 
grade  correlations  and  sex  differences  will  then  be  taken  up  in 
detail. 


11.    SUBJECTS  AND  METHODS 

Subjects 
The  data  which  are  here  analysed  to  determine  the  influence 
of  the  personal  equation,  of  grade  training  and  of  sex  differ- 
ences, are  derived  from  all  the  boys  and  girls  below  the  seventh 
grade  in  the  Princeton,  N.  J.,  Model  School.  This  group  in- 
cludes 422  subjects  of  the  following  age  distribution, — 

Chronological  Ages. 
4        5        6        7        8        9      10      II      12      13      14      15      16 
4      17      62      52      56      42      53      49      36      32      II        62 

Each  of  the  first  six  school  grades  was  divided  into  a  plus 
and  minus  grade,  the  latter  division  being  under  a  different 
teacher,  and  containing  those  who  were  either  backward,  or,  on 
account  of  illness,  change  of  school,  or  for  reasons  not  neces- 
sarily related  to  their  mental  development,  were  not  sufficiently 
advanced  to  perform  the  work  of  their  grade.  The  school  also 
contained  a  special  class  for  defective  and  exceptionally  back- 
ward children.  The  subjects  were  distributed  in  the  school 
grades  as  follows, — 

School  Grades. 

Spec.  Kind  I—    1+  II—  11+  HI—  III+  IV—  IV+  V—    V+  VI—  VI+ 

18        32      38      51     12      40       12       45     15        35       IS       49      II        49 

39  or  9.2%  of  the  subjects  were  children  of  non-English  speak- 
ing parents,  this  group  including  6.6%  of  the  children  in  the 
Kindergarten  and  first  six  regular  grades,  and  15.7%  of  those 
in  the  special  class  and  minus  grades. 

The  selection  of  subjects  is  only  fairly  typical  of  the  general 
run,  for  Princeton  has  no  manufactories.  The  children  examined 
came,  for  the  most  part,  from  the  homes  of  laborers,  domestics, 
artisans,  farmers,  tradesmen,  clergymen  and  college  professors. 
The  selection  is  atypical  in  that  none  of  the  children  came  from 
homes  of  the  manufacturing  class,  while  an  unusually  large  pro- 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  9 

portion  came  from  the  homes  of  those  engaged  in  domestic, 
personal,  and  professional  service. 

Tests 

The  scale  used  was  Goddard's  (28)  191 1  revision  of  the 
Binet-Simon  scale.  The  methods  used  in  giving  the  tests  were, 
as  far  as  possible,  the  same  as  those  outlined  by  Goddard  in  the 
original  revision,  incorporating  the  rules  and  suggestions  for 
standardized  scoring  published  by  that  writer  (29)  in  19 13. 
The  methods  used  will  not  be  discussed  in  detail,  for  the  data 
are  not  used  in  obtaining  age  norms  and  standards  for  children 
generally.  For  the  analysis  of  the  data  in  terms  of  grade  and 
sex  it  is  not  necessary  that  the  procedure  should  be  absolutely 
standardized,  but  that  the  experimenters  who  gave  the  tests 
should  have  used  the  same  procedure.  Differences  in  the  tech- 
nique of  the  experimenters  will  be  discussed  in  the  chapter  on 
the  personal  equation. 

One  variation  frorh  the  usual  procedure  was  adopted.  In  no 
case  did  the  experimenter  know  the  chronological  age  of  the 
child  being  tested.  The  influence  of  any  prejudice  or  bias  on 
the  part  of  the  experimenter  is  therefore  eliminated  from  the 
problem  of  the  correlation  of  the  tests  with  age.  The  three  ex- 
perimenters who  gathered  the  material  in  the  spring  of  1913 
examined  the  sixth  grade  first  and  the  remaining  grades  in  de- 
creasing order.  During  the  school  year  19 13- 19 14,  the  fourth 
experimenter  examined  all  children  at  that  time  in  the  kinder- 
garten and  first  grades,  and  others  who  were  not  examined  in 
the  spring  of  1913. 

The  tests  in  the  "three  year",  "four  year",  "five  year",  "fifteen 
year"  and  "adult"  groups  were  given  so 'in frequently  that  the 
data  from  them  are  not  treated.  The  tests  used  are  as  follows. 
The  figure  at  the  right  shows  the  total  number  of  times  each 
test  was  given. 

AGE  VI 

1.  Distinguishing  between  morning  and  afternoon 108 

2.  Defining  in  terms  of  use 333 

3.  Executing  three  commissions 100 


lo  CARL  C.  BRIGHAM 

4.  Showing  right  hand  and  left  ear 107 

5.  Choosing  the  prettier  of  given  faces 117 

AGE  VII 

1.  Counting  13  pennies 217 

2.  Describing  pictures 219 

3.  Indicating  omissions   in  pictures 217 

4.  Copying  the  diamond  (in  pencil) 225 

5.  Naming  four  colors 218 

AGE  VIII 

1.  Comparing  remembered  objects  (butterfly  and  fly) 271 

2.  Counting  backwards  from  20  to  0 251 

3.  Enumerating  the  days  of  the  week 277 

4.  Counting    stamps 258 

5.  Repeating  5   digits 413 

AGE  IX 

1.  Making  change 271 

2.  Defining  in  terms  superior  to  use 333 

3.  Giving  the  day  and  date 307 

4.  Enumerating   the    months 284 

5.  Arranging  five  weights 334 

AGE  X 

1.  Recognizing  pieces  of  money 282 

2.  Copying  designs  from  memory 252 

3.  Repeating  6  digits 413 

4.  Comprehending  easy  and  difficult  questions 250 

5.  Using  three  words  in  sentence  (two  ideas) 279 

AGE  XI 

1.  Detecting  absurdities  in  statements 226 

2.  Using  three  words  in  sentence  (one  idea) 279 

3.  Giving  60  words  in  three  minutes 233 

4.  Giving  rhymes  with  day,  mill  and  spring 213 

5.  Reconstructing  dissected   sentences 190 

AGE  XII 

1.  Repeating  7  digits 413 

2.  Defining  abstract  terms 144 

3.  Repeating  a  sentence  of  28  syllables 169 

4.  Resisting  suggestion    (length  of  lines) 203 

5.  Solving  problems  from  various  facts 123 

The  tests  in  the  "six  year"  group,  with  the  exception  of  de- 
fining in  terms  of  use,  and  the  tests  in  the  "twelve  year"  group, 
with  the  exception  of  repeating  7  digits,  were  given  so  infre- 
quently or  so  irregularly  that  the  data  from  them  could  not  be 
treated.  The  apparatus  used  in  the  test  of  arranging  five  weights 
was  not  constant  throughout  the  experiment,  the  standard  cubes 


VARIABLE  FACTORS  IX  THE  BIXET  TESTS  ii 

and  weighted  pill  boxes  being  used  at  different  times  by  different 
experimenters.  On  this  account,  the  data  from  this  test  are 
not  included  in  the  subsequent  discussion. 

Methods  of  Treating  Results 

The  chronological  age  of  each  subject  was  taken  as  that  at 
the  last  birthday,  one  tenth  of  a  year  being  allowed  for  each 
36  days  beyond  the  birthday.  The  subject  that  was  10  years 
and  35  days  would  be  rated  lo.o  years,  while  ten  years  and  36 
days  would  be  10.  i  years.  A  subject  one  .day  short  of  11  would 
be  rated  10.9  etc.  The  teachers  of  each  grade  submitted  the 
dates  of  birth  of  all  pupils  after  the  grade  had  been  tested. 
These  data  were  later  checked  up  from  the  entrance  cards.  Since 
the  purpose  of  this  study  is  to  analyze  the  factors  involved  in 
the  individual  tests,  no  "mental  ages"  or  total  scores  were  fig- 
ured. The  classifications  of  the  subjects  are  all  made  independ- 
ently of  the  tests. 

Two  measures  of  central  tendency  will  be  used  in  the  subse- 
quent discussion,  the  average  and  the  median.  The  measure 
of  variability  from  the  average,  that  will  be  used,  is  the  mean 
variation  (or  average  deviation),  the  average  of  the  differences, 
regardless  of  signs,  between  the  separate  measures  in  the  series 
and  the  average  of  the  whole  series.  The  measure  of  variability 
from  the  median  that  will  be  used  is  the  semi-interquartile  range 
(Q),  or  half  the  difference  between  the  measure  with  three 
times  as  many  measures  above  as  below  it  and  the  measure  with 
one  third  as  many  measures  above  as  below  it,  i.  e.  half  the 
difference  between  the  25  percentile,  and  the  75  percentile.  Any 
coefficients  of  correlation  used  will  be  stated  in  terms  of  the 
formula  applied.  The  reader  is  referred  to  Thorndike  (70)  for 
the  discussion  and  explanation  of  the  statistical  measures  used. 

The  measures  of  ability  in  most  of  the  tests  are  in  the  "all 
or  none"  form — the  tests  are  either  passed  or  failed.  The  only 
measure  that  can  be  obtained  from  data  of  this  sort  is  the  per- 
centage that  an  ability  is  present  in  a  defined  group.  This 
method  of  treating  the  results  has  as  many  "pit-falls"  as  the 
tests  themselves.    Before  undertaking  the  analysis  of  the  Prince- 


12  CARL  C.  B  RICH  AM 

ton  data  to  determine  the  effect  of  the  personal  equation  of  the 
experimenter,  and  the  age,  grade,  and  sex  of  the  subject  upon 
the  results  of  the  individual  tests,  it  is  necessary  to  consider 
an  error  which  underlies  incomplete  data,  or  those  data  derived 
from  experimenting  in  which  every  test  is  not  given  to  every 
subject. 

No  uniform  instructions  were  given  to  the  experimenters  con- 
cerning the  order  in  which  the  tests  should  be  given,  nor  the 
number  of  tests  that  should  be  tried.  The  experimenters  at- 
tempted to  determine  the  mental  age  of  the  child  according  to 
the  scale.  In  doing  this  they  would  start  with  some  test  which 
they  considered  would  be  interesting  to  the  child,  and,  at  the 
same  time,  well  within  his  reach.  The  tests  given  first  were 
usually  those  of  describing  pictures  and  arranging  five  weights. 
The  experimenter  would  then  gradually  explore  the  subject's 
range  of  ability,  varying  the  order  of  the  tests  so  as  to  maintain 
the  subject's  interest,  and  to  ward  off  fatigue.  In  this  way  the 
experimenter  would  eventually  establish  the  basal  age  of  the 
subject  (that  age  in  which  he  passed  all  five  of  the  tests),  and 
by  the  end  of  the  examination  would  have  tried  all  the  tests 
above  the  basal  age  which,  in  his  judgment,  there  was  any  possi- 
bility of  the  subject's  passing.  This  method  of  experimenting 
will  be  called  incomplete.  The  other  method  of  experimenting, 
in  which  a  certain  number  of  tests  are  adopted  and  all  of  the 
tests  are  tried  on  each  subject,  will  be  called  complete.  Each 
experimenter  in  the  Princeton  investigation  averaged  19  or  20 
tests  to  a  subject.  In  the  Trenton  investigation  all  the  tests  were 
given  to  all  the  subjects. 

The  incomplete  method  is  more  desirable  from  the  standpoint 
of  the  subject  who  is  not  unnecessarily  fatigued,  and  from  the 
standpoint  of  the  experimenter,  as  well,  who  saves  in  the  ex- 
penditure of  time  and  energy.  However,  the  data  derived  from 
the  incomplete  method  are  subject  to  an  error,  which,  unless  it  is 
properly  considered,  will  completely  vitiate  the  results. 

When  the  experimenter  does  not  try  a  test  above  the  basal 
age  because  he  believes  that  the  subject  will  not  pass  it,  he  im- 
plies that  the  subject  will  fail  it.     This  amounts  to  a  failure. 


VARIABLE  FACTORS  IN  THE  BIXET  TESTS  13 

for  the  subject  receives  no  credit.  However,  a  failure  of  this 
sort,  due  to  the  experimenter's  assumption,  is  not  the  same  as 
an  actual  failure  in  which  the  test  is  tried,  for  there  is  always 
the  possibility  that  the  assumption  was  unjustified.  In  like  man- 
ner when  the  experimenter  does  not  try  tests  below  the  basal 
age,  he  actually  gives  credit  for  passing  the  test  without  the 
actual  trial. 

In  some  cases  the  assumption  on  the  part  of  the  experimenter 
is  quite  justified.  Obviously  if  a  subject  can  make  change,  he 
can  count  up  to  thirteen;  if  he  can  repeat  seven  digits,  he  can 
repeat  five  and  six  digits;  if  he  knows  the  names  of  the  months, 
he  will  know  the  days  of  the  week;  and,  conversely,  if  he  cannot 
repeat  the  days  of  the  week,  he  cannot  repeat  the  months.  Other 
assumptions  are  less  justifiable.  Since  very  intelligent  persons, 
lacking  in  particular  sorts  of  abilities,  might  fail  in  tests  such 
as  drawing  the  design  from  memory  or  arranging  five  weights, 
there  is  no  reason  for  supposing  that  a  subject  making  basal 
"eleven"  or  "twelve"  will  pass  these  tests.  At  the  same  time 
there  is  no  reason  for  assuming  that  a  subject  failing  to  estab- 
lish basal  "seven"  for  instance,  will  fail  to  pass  a  test  such  as 
the  line  suggestion  test  in  "twelve".  The  assumptions  of  the 
experimenters,  then,  are  more  or  less  justifiable  and  it  is  im- 
possible to  estimate  the  amount  of  the  justification,  since  this 
is  dependent  on  the  nature  of  the  individual  tests. 

The  manner  in  which  this  error  works  out  in  the  statistical 
treatment  of  the  results  may  be  shown  by  examining  any  test 
which  has  been  tried  through  a  number  of  chronological  ages. 
Table  i  shows  the  results  of  the  60  w^ord  test  obtained  from 
subjects  7  to  13  years  of  age. 

TABLE  NO.  I 

Analysis  of  the  Results  from  the  Test  in  Naming  60  Words  in  3  Minutes. 

Chronological  ages    7  8  9  10  11  12        13 

No.  of  times  given 11         18  25  42  44  31        28 

No.  of  time  passed  4        10  10  24  34  19        21 

Actual  percentage  passed 36%     56%  40^0  57%  77%  61%     75% 

Total  number  of  subjects 60        52  42  54  48  36        28 

Percentage    of    subjects    to    whom 

test  was  given 18%     35%  60%  78%  92%  86%  100% 

Theoretical   percentage   passed 7%     19%  24%  44%  71%  53%  75% 


14  CARL  C.  BRIGHAM 

An  example  will  make  the  above  table  clear.  The  60  word 
test  was  given  to  11  subjects,  age  seven,  4  of  whom  passed. 
In  all  there  were  60  subjects  at  this  age,  so  that  the  11  subjects 
to  whom  the  test  was  given  constitute  but  18%  (and  probably 
the  brightest  18%)  of  this  whole  number.  The  percentage 
passed  would  have  been  7%  had  the  test  been  given  to  all  60 
subjects,  and  had  all  the  subjects  failed  who  the  experimenters 
assumed  would  fail  if  they  gave  the  test.  The  true  per  cent, 
which  represents  the  ability  of  non-selected  seven  year  boys  and 
girls  in  passing  the  60  word  test  therefore  lies  somewhere  be- 
tween 7%  and  36%,  probably  nearer  7%.  An  accurate  estimate 
of  the  real  per  cent,  which  will  represent  this  ability  is,  however, 
impossible.  In  like  manner,  the  ability  of  the  8  year  subjects 
is  represented  by  a  percentage  somewhere  between  19%  and  56%. 

As  the  proportion  between  the  number  of  subjects  in  the 
group  and  the  number  actually  tested  increases,  the  disparity  be- 
tween the  actual  and  theoretical  percentage  passed  becomes  less, 
or,  in  other  words,  the  results  which  express  the  ability  of  a 
group  become  more  reliable  as  the  number  of  individuals  actually 
tested  as  a  sample  of  this  group  becomes  larger.  The  higher 
the  percentage  given,  the  more  reliable  the  percentage  passed, 
when  the  reliability  is  measured  by  the  difference  between  the 
actual  percentage  passed  and  the  theoretical  percentage  passed. 

The  source  of  error  mentioned  causes  great  difficulty  in  com- 
paring the  results  of  different  investigators.  For  example,  it  is 
desired  to  compare  the  results  of  Terman  and  Childs  (66)  and 
Douglierty  (23)  with  those  of  this  investigation  on  the  60  word 
test.  Table  2,  derived  from  their  published  results,  shows  the 
percentage  that  the  test  was  given  of  the  number  of  times  it  was 
possible  to  be  given,  (%G),  the  actual  percentage  passed, 
(A%P),  and  the  theoretical  percentage  passed,  (T%P),  or  that 
percentage  passed  that  would  have  resulted  had  all  of  the  sub- 
jects failed,  who  it  is  necessary  to  suppose  would  have  failed, 
had  the  test  been  given  all  the  possible  number  of  times. 


VARIABLE  FACTORS  IX  THE  BIXET  TESTS 

TABLE  NO.  2 

Analysis  of  the  Results  of  Three  Investigators  on  the  60  Word  Test. 


This 

investigation 

Terman  and  Childs 

Dougherty 

Age 

%G 

A%P  T%P 

%G 

A%P 

T%P 

%G 

A%P  T%P 

7 

18 

36 

7 

14 

50 

7 

8 

35 

56 

19 

47 

35 

16 

IS 

0         0 

9 

60 

40 

24 

86 

57 

49 

35 

60        21 

10 

78 

57 

44 

100 

67 

78 

53        41 

II 

92 

77 

71 

98 

83 

82 

89 

79        70 

12 

86 

61 

53 

97 

82 

80 

91 

95        87 

13 

100 

75 

100 

94 

94 

88        83 

It  is  very  difficult,  if  not  impossible,  to  make  a  comparison  of 
these  results  shown  in  Table  2  for  the  years  7,  8  and  9.  The 
ability  of  Terman's  7  year  group  is  represented  by  a  figure  some- 
where between  7%  and  50%,  while  that  of  the  8  year  group  falls 
somewhere  between  16%  and  35%.  Dougherty's  9  year  group 
falls  between  21%  and  60%.  In  the  older  years  where  the  re- 
sults have  greater  reliability,  it  is  probable  that  the  discrepancies 
betw-een  the  investigators  could  be  accounted  for  on  the  basis 
of  the  inferiority  of  the  selection  of  the  older  subjects  in  this 
investigation,  the  other  investigations  including  children  from 
the  seventh  and  eighth  grades. 

In  order  to  make  a  comparison  between  investigators,  it  is 
necessary  to  express  the  results  in  terms  of  a  percentage  or  a 
proportion.  The  expression  of  the  ability  of  a  group  by  a  per- 
centage or  a  proportion  is  inaccurate  if  the  data  are  incomplete, 
and  in  order  to  judge  the  accuracy  of  the  data,  it  is  necessary 
to  know  the  degree  of  completeness.  Unfortunately,  the  results 
of  most  of  the  investigations  on  the  individual  tests  are  not  pub- 
lished in  a  form  that  enables  one  to  estimate  the  accuracy  of  the 
data.  The  w-riters  who  have  published  their  data  in  a  form 
that  will  admit  of  this  treatment,  have  not  treated  the  sexes 
separately.  On  this  account,  the  writer  will  not  attempt  a  sys- 
tematic comparison  of  the  results  of  this  investigation  with  those 
of  other  experimenters. 

Before  analysing  the  Princeton  data  the  following  problem 
should  be  answered: — What  proportion  of  a  given  group  must 
actually  be  tested  for  an  ability  in  order  that  the  results  may  be 


i6  CARL  C.  BRIGHAM 

considered  as  typical  of  the  ability  of  the  whole  group?  The 
proper  proportion  to  select  as  typical  of  any  one  group  depends 
upon  the  characteristics  of  the  group  itself.  If  the  members 
of  a  group  are  similar,  a  smaller  proportion  would  stand  for 
the  ability  of  the  group  than  would  be  necessary  for  a  group 
composed  of  unlike  individuals.  A  smaller  number  of  individuals 
would  be  necessary  to  stand  for  the  ability  of  all  the  12  year 
boys  in  the  sixth  grade,  for  example,  than  for  all  the  12  year 
boys  coming  from  a  great  many  grades.  This  proposition  op- 
erates directly  counter  to  actual  practice,  for  the  members  of 
a  group  of  similar  individuals  will  be  given  similar  tests,  while 
unlike  individuals  will  receive  different  tests,  inasmuch  as  the 
experimenter  adapts  his  procedure  to  the  need  of  the  individual 
being  examined.  The  proposition  actually  means,  then,  that 
selected  results  from  incomplete  testing  are  more  reliable  than 
non-selected  results,  if  each  group  has  the  same  range  of  testing. 
The  proportion  of  a  group  that  must  be  tested  to  stand  for  the 
whole  group  will  also  vary  from  test  to  test.  In  some  tests  of 
particular  abilities,  no  proportion  will  accurately  stand  for  the 
whole  group — the  entire  group  must  be  tested.  In  other  tests 
that  are  easy  for  the  group,  the  results  of  a  very  small  proportion 
would  not  be  altered  by  examining  the  remainder  of  the  group. 

The  problem  of  deciding  what  proportion  of  a  given  group 
must  actually  be  tested  for  an  ability  in  order  that  their  results 
may  be  considered  as  typical  of  the  ability  of  the  whole  group 
has,  therefore,  no  answer  in  the  work.  The  writer  will  decide 
arbitrarily  what  the  proportion  will  be.  The  actual  magnitude 
of  the  proportion  between  the  number  actually  tested  and  the 
number  in  the  whole  group  (the  percentage  given)  will  always 
be  published  as  an  index  of  the  reliability  of  the  percentage  that 
the  group  passes  the  test  in  question. 

It  is  not  possible  to  obtain  reliable  results  showing  the  growth 
of  an  ability  with  age,  if  the  data  on  which  the  results  are  based 
are  of  the  incomplete  sort.  A  test  for  any  age  will  be  given  to 
a  superior  selection  of  subjects  below  that  age,  and  an  inferior 
selection  of  subjects  above  that  age,  so  that  the  growth  curve 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  17 

will  appear  flatter  than  it  actually  is.  For  this  reason,  the  Prince- 
ton data  may  not  be  used  for  the  purpose  of  standardizing  age 
norms. 

Binet  (4)  recognized  the  fallacy  of  calculating  proportions 
from  the  actual  number  of  times  a  test  was  given  and  passed 
when  the  test  had  not  been  given  all  the  possible  number  of  times. 
In  calculating  the  proportions  from  Levistre  and  Mode's  data, 
Binet  used  what  the  present  writer  would  call  the  "theoretical 
proportion  passed". 

It  has  been  shown  that  the  reliability  of  the  theoretical  per- 
centage passed  rests  on  the  accuracy  of  the  experimenters'  as- 
sumptions, and  that  according  to  the  nature  of  the  tests  and  the 
character  of  the  groups  to  which  they  are  given  these  assump- 
tions vary  from  complete  certainty  to  absolute  uncertainty. 
Inasmuch  as  these  assumptions  are  not  equally  certain,  the  con- 
clusions drawn  from  them  are  not  equally  certain,  and  the  logic 
of  scientific  method  demands  that  an  investigator  establish  the 
degree  of  certainty  of  his  conclusions.  In  this  case  the  measure 
of  the  degree  of  certainty  is  the  magnitude  of  the  percentage 
given. 

The  use  of  the  theoretical  percentage  passed  without  reference 
to  the  percentage  given  ignores  the  dictum  that  an  investigator 
establish  the  degree  of  certainty  of  his  conclusions,  and  sets  up 
all  conclusions  as  equally  valid,  a  procedure  which  in  actual  prac- 
tice results  in  making  all  conclusions  equally  invalid  when  the 
fact  of  degrees  of  certainty  is  admitted.  The  investigator  who 
draws  conclusions  from  incomplete  data  should  always  state  the 
percentage  given  and  the  actual  percentage  passed.  This  much 
at  least  is  experiment.  The  only  legitimate  use  of  the  theoretical 
percentage  passed  is  when  it  is  compared  with  the  actual  per- 
centage passed  as  a  probable  limiting  value.  The  theoretical 
percentage  passed  alone  has  no  claim  to  reliability. 


III.    THE  PERSONAL  EQUATION 

Before  attempting  to  correlate  the  individual  tests  with  age, 
grade  and  sex,  it  is  necessary  to  demonstrate  the  presence  or 
absence  of  the  effect  of  the  personal  equation.  By  the  term 
"personal  equation"  is  meant  the  complex  of  variable  factors 
which  are  independent  of  the  mental  make-up  of  the  subject  and 
the  environmental  conditions  at  the  time  of  the  examination. 
The  term  includes  such  widely  different  factors  as  the  experi- 
menter's ability  to  obtain  the  cooperation  of  the  subject,  his  pro- 
cedure in  giving  the  tests,  his  criteria  in  deciding  whether  a 
subject's  response  should  pass  or  fail,  and  the  tests  used,  insofar 
as  the  selection  of  tests  and  the  construction  of  the  apparatus 
were  occasionally  left  to  his  discretion,  apart  from  the  uniform 
procedure. 

The  only  method  of  detecting  the  influence  of  the  personal 
equation  in  most  of  the  tests  is  that  in  which  the  responses  of 
similar-  groups  of  subjects  to  different  experimenters  are  com- 
pared. On  account  of  the  wide  variations  in  the  character  of 
the  subjects  examined,  it  is  not  possible  to  compare  similar 
groups.  On  some  tests,  however,  it  is  possible  to  determine  the 
effect  of  the  personal  equation  independently  of  the  method  of 
group  comparison.  The  results  of  the  tests  that  may  be  studied 
independently  will  be  discussed  at  some  length,  in  order  to  dem- 
onstrate the  fact  that  certain  tests  are  susceptible  to  this  influence. 

The  examinations  of  the  Princeton  subjects  were  made  by 
four  experimenters,  called  for  convenience  A,  B,  C  and  D.  None 
of  the  experimenters  was  highly  trained  in  giving  the  tests, 
although  they  had  all  been  trained  in  the  methods  of  psycho- 
logical experimentation,  one  experimenter  being  an  assistant  pro- 
fessor of  psychology,  and  the  other  three  graduate  students  of 
psychology  of  at  least  one  year's  standing.  B,  C  and  D  per- 
formed their  experiments  at  the  same  time,  in  the  spring  of 
19 1 3,  while  A  experimented  one  year  later.    B,  C  and  D  studied 


rARIABLE  FACTO  US  IX  THE  BIXET  TESTS 


19 


the  scale  together  so  that  it  was  possible  to  secure  a  correspond- 
ence in  method.  At  the  close  of  practically  every  day's  testing, 
B,  C  and  D  would  confer  on  the  questions  brought  out  by  the 
day's  work,  and  as  far  as  possible  would  adopt  uniform  methods 
of  procedure  and  scoring.  A  was  subsequently  trained  in  these 
same  methods. 

In  spite  of  the  attempt  to  adopt  uniform  methods,  there  were 
a  few  tests  which  always  caused  difficulty,  and  concerning  which 
the  experimenters  could  reach  no  definite  agreement.  One  of 
the  tests  that  caused  the  greatest  difficulty  was  that  of  defining 
in  terms  of  use  and  in  terms  superior  to  use.  The  hierarchy  of 
responses  to  this  test  could  be  fairly  arranged  as  follows.  To 
the  question  "What  is  a  chair?"  the  following  typical  responses 
would  be  obtained,— I,  "A  chair  is  a  chair."  2,  "This  is  a 
chair."  3,  "x\  chair  is  to  sit  on."  4,  "A  chair  is  what  you  sit 
on."  5,  "A  chair  is  a  thing  you  sit  on."  6,  "A  chair  is  a  piece 
of  furniture  you  sit  on."  7,  "A  chair  has  four  legs,  a  back,  etc." 
8,  "A  chair  is  a  piece  of  furniture  with  four  legs,  a  back,  etc." 
Any  of  the  objects  for  which  a  definition  is  asked  (fork,  table, 
chair,  horse,  mother)  may  be  defined  by  repetition,  by  demon- 
stration, by  indicating  the  use  to  which  it  is  put,  by  showing 
the  class  to  which  it  belongs,  by  describing  its  parts,  or  by  the 
combination  of  any  or  all  of  these  methods. 

The  only  problem  is  to  decide,  arbitrarily,  how  definitely  the 
class  must  be  indicated  (i.  e.  by  "what",  "a  thing"  or  "a  piece  of 
furniture")  in  order  to  have  the  definition  considered  as  one  of 
classification.  The  rule  adopted  in  this  study  was  to  consider 
"thing"  as  indicating  the  class.  Nos.  i  and  2,  definitions  by 
repetition  and  demonstration,  received  no  credit  in  "six  years". 
Nos.  3  and  4  were  given  credit  in  "six  years"  as  definitions  by 
use,  and  nos.  5,  6,  7,  and  8  were  given  credit  in  "nine  years"  as 
definitions  in  terms  superior  to  use. 

In  studWug-  the  ranks  given  to  the  responses  of  the  subjects 
in  this  test,  it  was  found  that  the  experimenters  did  not  record 
the  responses  all  of  the  time.  A  gave  the  test  94  times,  and 
recorded  the  responses  66%  of  this  number.  B  gave  the  test 
98  times,  recording  the  subject's  answer  67'y^c  of  the  time.     C 


^o  CARL  C.  BRIGHAM 

gave  the  test  65  times,  and  recorded  the  answer  in  95%  of  the 
cases,  while  D  gave  the  test  76  times  and  recorded  the  response 
only  once. 

By  ranking  the  recorded  responses  of  A,  B  and  C  according 
to  the  rules  shown  above,  it  is  possible  to  obtain  an  estimate  of 
the  relative  severity  of  their  criteria  in  marking  these  responses 
plus  or  minus.  19%  of  A's  definitions  were  corrected,  the  cor- 
rection in  all  cases  being  from  minus  to  plus.  11%  of  B's 
definitions  were  corrected,  all  of  the  corrections  being  from  plus 
to  minus.  iy%  of  C's  definitions  were  corrected,  three  fourths 
of  them  being  changed  from  plus  to  minus,  and  one  fourth  from 
minus  to  plus.  C's  standards  changed  during  the  course  of  the 
experiment,  so  that  at  first,  with  older  subjects,  he  was  too 
lenient,  while  later,  with  younger  subjects  he  was  slightly  too 
severe.  The  tendencies  of  A  and  B  remain  constant  throughout 
the  experiment,  A  marking  too  severely  and  B  slightly  too  len- 
iently. The  differences  between  the  experimenters  hold  constant 
for  both  sexes.  The  experimenters  agreed  on  all  definitions  by 
use,  the  cases  of  disagreement  coming  on  the  definitions  superior 
to  use. 

One  test  in  which  variations  between  the  experimenters  might 
be  expected  is  that  of  copying  the  diamond.  In  this  test,  al- 
though the  apparatus  and  procedure  were  the  same,  the  experi- 
menters had  very  little  to  guide  them  in  forming  their  judgments 
of  passed  and  failed.  The  instructions  given  ("The  result  is 
considered  satisfactory  if  it  would  be  recognized  as  intended 
for  a  diamond  shaped  figure"),  and  the  examples  published 
furnish  very  vague  criteria. 

In  order  to  determine  the  effect  of  the  personal  equation  of 
the  experimenters  in  giving  credit  on  this  test,  all  of  the  repro- 
ductions of  the  diamond  obtained  in  the  Princeton  and  Trenton 
experimenting,  (311  in  number),  were  first  transcribed  and  then 
ranked.  On  the  sheet  containing  the  copy  only  the  subject's 
number  was  placed,  so  that  the  person  ranking  the  reproductions 
was  in  ignorance  of  the  experimenter  by  whom  it  was  obtained, 
the  mark  that  the  experimenter  had  given  it,  and  the  age,  grade, 
sex,  etc.  of  the  subject.     The  311  diamonds  were  then  classified 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  21 

into  six  groups  by  one  observer.  The  classification,  at  best,  was 
vague  and  indefinite,  but  it  represented  the  unbiased  judgment 
of  a  single  person.  Inasmuch  as  the  reproductions  were  classified 
and  re-classified  a  great  many  times,  small  errors  in  the  classifi- 
cation would  be  counterbalanced. 

The  first  group  contained  fairly  accurate  reproductions  of  the 
original,  diamonds  of  approximately  the  same  size  as  the  copy, 
having  the  sides  and  opposite  angles  nearly  equal,  and  with  a 
proper  proportion  between  length  and  width.  The  second  group 
contained  figures  inferior  to  those  of  the  first  group  in  size  or 
symmetry,  but  representing  a  fairly  high  grade  of  ability.  The 
reproductions  that  were  less  symmetrical  than  those  of  the  second 
group  were  classified  in  the  third  and  fourth  groups.  Figures 
showing  some  inequality  between  length  and  width  were  classified 
in  the  third  group,  while  those  of  approximately  unit  proportion, 
square  shaped  figures,  were  classified  in  the  fourth  group.  The 
reproductions  placed  in  the  fifth  group  were  figures  less  sym- 
metrical than  those  of  the  fourth  group,  and  figures  which  had 
curved  sides  and  rounded  corners.  The  sixth  group  contained 
all  figures  which  it  would  have  been  difficult  to  have  recognized 
as  intended  for  a  diamond,  figures  having  three,  five  or  more 
sides,  circles,  elipses,  unfinished  lines  and  eccentric  figures. 

The  above  classification  did  not  offer  an  opportunity  for  a 
sharp  grading  between  one  group  and  another,  but  in  general, 
the  reproductions  placed  in  the  various  groups  from  the  first  to 
the  sixth,  represented  a  decrease  in  the  ability  to  copy  the  dia- 
mond. The  justification  of  the  method  was  not  in  the  accuracy 
of  the  classification,  but  in  the  fact  that  the  material  was  all 
classified  by  one  observer  (B),  in  such  a  way  that  he  was  in 
ignorance  of  the  original  rank  that  had  been  given  the  repro- 
duction, of  the  experimenter  who  graded  it,  and  of  the  character 
of  the  subject. 

16%'  of  the  reproductions  were  classified  in  the  first  group, 
21%  in  the  second  group,  20%  in  the  third  group,  17%  in  the 
fourth  group,  9%  in  the  fifth  group,  and  17%  in  the  sixth  group. 
(The  irregularity  of  the  distribution  is  due  to  the  presence  of 
the  diamonds  drawn  by  the  Trenton  subnormal  group.) 


22  CARL  C.  B  RICH  AM 

After  classifying  all  of  the  reproductions  the  ranks  given  to 
them  by  the  different  experimenters  were  then  compared  with 
the  group  in  which  they  were  classified.  That  the  sliding  scale 
classification  used  represented  real  dift'erences  between  the  re- 
productions is  shown  by  the  relative  certainty  of  the  experi- 
menters' judgments.  None  of  the  reproductions  classified  in 
the  first  and  second  groups  were  ranked  as  failed  by  the  four 
experimenters,  while  only  one  reproduction  in  the  third  group 
was  ranked  minus.  i8%  of  the  fourth  group,  45%  of  the  fifth 
group  and  ^7%  of  the  sixth  group  were  ranked  as  failures.  All 
of  the  sixth  group  diamonds  that  were  ranked  plus  (23%),  were 
so  ranked  by  one  experimenter,  A. 

To  obtain  a  general  estimate  of  the  relative  severity  of  the 
experimenters'  criteria  in  making  their  judgments  of  passed  or 
failed,  the  diamonds  obtained  by  each  experimenter  from  boys 
and  girls  were  classified  according  to  rank,  plus  or  minus,  and 
according  to  their  group  in  the  classification.  From  this  it  was 
possible  to  obtain  an  estimate  of  the  passing  mark  of  each  ex- 
perimenter. For  example,  the  boys  of  experimenter  B  passed 
the  test  72%  of  the  time  according  to  his  ranking.  Had  B  given 
credit  for  the  first  five  groups  and  failed  only  the  reproductions 
in  the  sixth,  i.  e.,  had  his  passing  mark  been  the  fifth  group. 
88%  would  have  passed.  Had  his  passing  mark  been  the  fourth 
group,  81%  would  have  passed.  If  it  had  been  the  third  group, 
72%  would  have  passed,  while  only  56%  would  have  passed  had 
it  been  the  second  group.  Since  72%  of  B's  subjects  actually 
passed  the  test,  his  passing  mark  was  the  third  group — in  the 
long  run,  he  would  pass  all  diamonds  in  the  first  three  groups 
and  fail  all  in  the  last  three.  The  differences  between  the  experi- 
menters on  this  basis  are  quite  marked.  The  passing  mark  for 
C  and  D  was  the  fourth  group,  while  A's  passing  mark  was  the 
fifth  group.  B  was  the  most  severe,  and  A  was  the  most  lenient, 
with  C  and  D  between  the  two.  The  results  were  the  same  for 
both  sexes. 

Another  test  in  which  the  influence  of  the  personal  equation 
might  be  looked  for  is  that  of  copying  designs  from  memory. 
The  experimenter  must  here  use  his  own  judgment  in  marking 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  23 

the  designs  passed  or  failed.  Very  little  guidance  is  given  by 
Binet's  rule,  which  reads,  "The  test  is  considered  passed  when 
one  of  the  designs  is  reproduced  exactly,  and  half  of  the  other 
is  correctly  drawn",  or  by  the  interpretation  of  this  "half  right" 
as  applying  "when  two  component  parts  are  transposed  or  one 
component  part  omitted". 

In  order  to  test  the  experimenters'  judgments  in  ranking  this 
test,  a  scoring  system  was  devised,  which  may  be  explained  by 
reference  to  Figure  i,  which  gives  the  original  copy  and  various 
duplicated  portions.  In  scoring  the  reproductions  of  the  pyramid 
section,  5  points  were  given  when  the  reproduction  of  the  asym- 
metry of  the  figures  was  nearly  exact,  as  in  no.  i,  4  points  for 
a  less  perfect  reproduction  as  in  no.  2,  and  3  points  for  a  repro- 
duction in  which  the  rectangle  fell  in  the  center  of  the  figure, 
as  in  no.  3.  i  point  was  deducted  from  this  score  for  each 
failure  to  connect  the  corners  of  the  rectangles  as  in  no.  4  (which 
is  modified  from  no.  3  and  would  therefore  receive  only  i  point), 
and  no  credit  was  allowed  for  "boxes'"  (no.  5),  and  other  eccen- 
tric figures. 

In  scoring  the  more  complicated  design,  4  points  were  allowed 
for  each  of  the  "posts",  ABCDE  and  JKLMN,  or  no.  6.  2  points 
were  deducted  for  turning  them  in  the  wrong  direction  as  in 
no.  7,  (which  is  "post"  ABCDE  turned  in  the  wrong  direction), 
2  points  for  failure  to  make  the  line  AB  penetrate  DE  as  in 
no.  8,  so  that  a  combination  of  these  errors,  as  in  no.  9,  would 
receive  no  credit,  along  with  other  eccentric  reproductions  as 
in  nos.  10  A,  B,  C,  D,  E  and  F.  i  point  was  given  for  each 
of  the  lines  EF  and  IJ,  and  5  points  for  the  "hump",  FGHI. 
A  continuous  line  from  E  to  J  as  in  no.  11  would  therefore  re- 
ceive no  credit,  while  a  division  of  the  lines,  without  the  portion 
FGHI,  as  in  nos.  12  or  13,  would  receive  2  points.  An  accurate 
reproduction  of  the  portion  EFGHIJ,  as  in  no.  14,  would  receive 
full  credit  for  all  parts,  7  points,  no  credit  being  allowed  for 
eccentric  reproductions  of  the  "hump"  as  in  nos.  15  A,  B,  C 
and  D. 

The  maximum  credit  for  the  test  is  20  points,  divided  between 
the  two  figures  on  the  proportion  of  5  to  15,  a  fair  proportion 


24 


CARL  Q.  BRIG  HAM 


0  c    q H   L  K 

E       F         I        J 

P- 


6         7      8       9 


10    A  B  C    D  E      F 


15      A       B         CD 

Fig.  I.     Method  of  Scoring  Test  of  Copying  Designs  from  Memory 

(in  the  writer's  opinion)  according  to  the  relative  difficulty  of 
the  parts.  A  design  with  "one  component  part  omitted"  would 
be  scored  13  points  according  to  this  system,  and  one  with  "two 


/  -JRIABLE  FACTORS  IX  THE  BIXET  TESTS  25 

component  parts  transposed",  16  points,  provided  that  the  repn;- 
ductions  of  the  pyramid  section  were  perfect  in  each  case. 

All  the  reproductions  of  the  designs  obtained  from  the  Prince- 
ton and  Trenton  experimenting  were  then  scored  according  to 
this  system.  The  score  of  each  subject  of  each  experimenter 
in  the  Princeton  series  was  then  compared  with  the  experi- 
menter's ranking,  which  was  recorded  on  the  same  sheet,  and 
which  was  not  seen  at  the  time  the  designs  were  graded  by  the 
point  system.  From  the  number  of  times  the  test  was  given, 
and  the  number  of  times  it  was  marked  passed  by  the  experi- 
menter, the  percentage  passed  was  obtained  for  each  experi- 
menter for  both  sexes.  The  scores  from  all  the  designs  from 
o  to  20  were  then  classified  according  to  the  judgment  passed  or 
failed  as  given  by  each  experimenter  on  subjects  of  both  sexes. 
It  was  found  that  there  were  certain  ranges  where  the  experi- 
menters' judgments  coincided  accurately,  i:  e.  in  the  very  low 
scores  and  in  the  very  high  scores.  A  certain  range  existed, 
approximately  from  10  to  15  points,  in  which  the  same  results 
would  sometimes  be  ranked  as  passed  and  failed  by  the  same 
experimenter  at  different  times. 

It  was  possible,  however,  to  obtain  a  general  estimate  of  the 
experimenters'  criteria  by  a  method  similar  to  that  used  in  the 
study  of  the  diamond  test.  For  example,  B  gave  the  test  to 
boys  48  times,  passing  40%  of  them.  Had  his  passing  mark 
been  18  (i.  e.  had  he  passed  all  subjects  whose  designs  scored 
18  points  or  better),  21%  would  have  passed.  Had  his  passing 
mark  been  15  points,  35%  would  have  passed.  Had  it  been  13, 
42%  would  have  passed  etc.  B's  passing  mark  would  therefore 
fall  between  13  and  15  points.  In  this  way,  by  calculating  the 
percentage  passed  at  each  score  for  each  experimenter  for  both 
sexes,  it  was  possible  to  obtain  the  passing  mark  of  each  group. 
The  passing  marks  coincided  very  closely  except  in  one  case. 
With  one  exception  the  passing  marks  were  around  12,  13,  14 
or  15  points,  for  the  boys  and  girls  of  all  experimenters,  i.  e. 
the  experimenters  would,  in  the  long  run,  rank  all  below  this 
level  minus  and  all  above  this  level  plus.  The  degree  of  cor- 
respondence was  quite  remarkable  considering  the  fact  that  the 


26  CARL  C.  BRIGHAM 

experimenters  had  very  little  on  which  to  base  their  judgments. 

The  one  exception  is  both  striking  and  suggestive.  C's  pass- 
ing mark  for  boys  was  15  points,  for  girls  8  points.  In  order 
to  receive  a  plus  from  C,  boys  would  have  to  draw  a  much  more 
accurate  design  than  girls,  or,  in  other  words,  a  very  faulty 
reproduction  drawn  by  a  girl  would  receive  credit,  w^hile  the 
same  reproduction  if  drawn  by  a  boy  would  invariably  be  failed. 
This  deviation  rests  on  a  small  number  of  cases.  A  gave  the 
test  to  24  boys  and  21  girls,  B  to  48  boys  and  33  girls,  C  to  28 
boys  and  22  girls,  and  D  to  36  boys  and  31  girls.  A's  results, 
although  resting  on  a  number  of  cases  as  small  as  C's,  show  no 
such  deviation  as  those  of  the  latter.  On  account  of  the  small 
number  of  cases,  this  finding  cannot  be  considered  definite.  It 
does,  however,  suggest  the  possibility  of  a  difference  in  the  ex- 
perimenters' reaction  to  the  sexes.  An  experimenter  may  show 
greater  leniency  to  one  sex  than  to  the  other,  so  that  a  supposed 
sex  difference  may  be  the  results  of  an  experimenter's  reaction 
to  the  sex,  rather  than  the  sex's  reaction  to  a  test. 

The  test  of  using  three  words  in  a  sentence  ("Philadelphia, 
money  and  river")  was  given  279  times,  and  the  sentences  given 
by  the  subjects  were  recorded  over  half  the  time.  Experimenter 
A  gave  the  test  53  times,  recording  the  result  36%  of  the  time. 
B  gave  the  test  95  times,  recording  the  answer  in  92%  of  the 
cases.  C  gave  the  test  56  times,  recording  the  answer  23%  of 
that  number,  and  D  gave  the  test  75  times,  recording  the  response 
in  43%  of  the  cases. 

To  obtain  a  check  on  the  accuracy  of  the  experimenters'  scor- 
ing of  this  test,  all  of  the  recorded  sentences  were  transcribed  so 
that  they  could  be  studied  and  ranked  without  reference  to  the 
subject  or  the  experimenter.  The  162  recorded  sentences  were 
then  marked  plus  or  minus  by  one  observer  (B).  This  ranking 
was  checked  several  times  and  then  compared  with  the  original 
ranking. 

There  was  no  disagreement  between  the  judgments  of  the 
four  experimenters  and  the  one  impartial  observer  in  marking 
responses  for  the  "ten  year"  credit.  In  marking  for  the  "eleven 
year"  credit,  there  were  8  disagreements  out  of  the  162  judg- 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  ^ 

ments,  the  8  variations  being  evenly  distributed  among  the  ex- 
perimenters. It  may  be  concluded,  then,  that  the  influence  of 
the  personal  equation  is  absent  in  this  test,  although  there  is 
ample  opportunity  for  variation. 

The  detailed  study  of  the  foregoing  tests  has  shown  that  the 
personal  equation  of  the  experimenters  has  a  marked  effect  on 
the  results  of  some  of  the  tests.  In  the  subsequent  correlation 
of  the  tests  with  grade  and  sex  the  corrected  score  of  these  tests 
will  be  used.  Only  those  definitions  will  be  used  which  were  re- 
corded by  the  experimenters,  and  the  ranking  of  the  one  observer 
will  be  followed.  All  reproductions  of  the  diamond  in  the  fifth 
and  sixth  group  will  be  scored  as  failed,  the  others  as  passed. 
A  reproduction  of  the  designs  scoring  15  or  more  points  will 
be  ranked  as  passed.  The  corrected  results  of  the  sentence  test 
will  be  used. 

To  show  that  the  effect  of  the  personal  equation  of  the  experi- 
menter is  present  or  absent  in  the  tests  on  which  there  is  no 
actual  record  of  the  subject's  response,  is  a  more  difficult  prob- 
lem. The  most  reliable  method  of  showing  the  influence  of  this 
factor  is  that  in  which  the  reactions  of  similar  groups  of  sub- 
jects, examined  by  different  experimenters,  are  studied.  The 
greater  the  similarity  of  the  groups  the  more  reliable  the  results. 
If  two  experimenters  each  examined  50  boys  of  12  years  of  age 
from  the  sixth  grade,  their  results  should  compare  closely,  and 
any  difference  could  immediately  be  referred  to  a  difference  in  the 
personal  equation.  However,  if  one  examined  boys  from  this 
grade  and  the  other  girls,  the  variations  might  be  explained  on 
the  basis  of  sex  differences.  In  the  same  way  the  results  may 
vary  with  the  age  of  the  subject,  and  with  his  grade  and  nation- 
ality. 

It  is  not  possible  in  this  study  to  obtain  groups  of  a  sufficient 
degree  of  similarity,  in  spite  of  the  small  number  of  children 
of  non-English  speaking  parents,  and  the  fact  that  the  sexes  may 
be  treated  separately.  The  subjects  vary  in  age  from  4  to  16, 
and  in  grade  from  the  kindergarten  to  the  sixth  grade.  A  ex- 
amined a  very  much  younger  run  of  subjects  than  B,  C  and  D. 
The  data  of  the  four  experimenters  were  treated  by  three  meth- 


28  CARL  C.  BRIG  HAM 

ods,  by  comparing  the  per  cent,  that  all  boys  and  girls  of  each 
experimenter  passed  each  test,  by  comparing  the  per  cent,  that 
selected  subjects  of  each  experimenter  passed  each  test,  and  by 
comparing  the  per  cent,  that  all  subjects  from  5  to  9  and  from 
10  to  13  passed  each  test.  The  sexes  were  separately  treated  in 
each  method.  None  of  the  methods  proved  satisfactory,  and  it 
was  found  to  be  impossible  to  obtain  an  accurate  quantitative 
estimate  of  the  ef¥ect  of  the  personal  equation  on  each  test.  In 
certain  of  the  tests,  however,  there  were  known  differences  of 
procedure  which  might  have  influenced  the  results,  while  the 
variations  in  the  results  of  certain  other  tests  were  so  striking 
that  definite  conclusions  could  be  drawn. 

One  possible  source  of  variation  was  the  use  of  alternative 
questions  in  several  of  the  tests.  When  an  entire  school  system 
is  examined,  and  the  children  learn  that  they  will  all  be  tested, 
the  possibility  is  always  present  that  they  will  inform  each  other 
of  the  nature  of  the  tests,  and  the  answers  to  some  of  the  ques- 
tions. The  alternative  questions  were  used  to  counteract  the 
influence  of  this  factor. 

In  the  test  of  detecting  absurdities  in  statements,  ten  or  eleven 
statements  were  used,  the  experimenter  choosing  the  five  that 
he  would  give  the  subject.  The  statements  varied  greatly  in 
difficulty  and  the  experimenters  did  not  use  the  same  selection 
throughout  the  experiment.  This  test  was  given  by  B  to  26 
girls  whose  average  age  was  10.6  years,  while  D  gave  the  test 
to  25  girls  whose  average  age  was  10.9  years.  65%  of  the  girls 
examined  by  B  passed  the  test,  while  only  36%  of  D's  group 
passed.  The  variation  between  the  experimenters  might  be  due 
to  the  selection  of  absurdities  of  unequal  difficulty,  or  to  different 
criteria  in  grading  the  responses.  The  sources  of  variation  are 
too  large  to  admit  of  obtaining  any  reliable  results  from  this  test 
in  correlating  it  with  grade  and  sex. 

75%  of  the  girls  to  whom  B  gave  the  test  of  reconstructing 
dissected  sentences  passed,  while  only  28%  of  C's  girls  passed. 
The  average  age  of  the  26  girls  to  whom  B  gave  the  test  was 
10.8  years,  and  the  average  age  of  C's  subjects  10.5  years.  Part 
of  the  difference  between  these  two  experimenters  is  due  to  the 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  29 

fact  that  more  of  B's  subjects  came  from  the  fifth  and  sixth 
school  grades.  Some  variation  might  have  been  due  to  different 
apparatus,  B  using  cards  with  the  sentences  printed  on  two  lines, 
while  C  had  the  sentences  typewritten  on  one  line.  The  sentences 
used  by  B  were  more  legible,  and,  being  broken  into  two  lines, 
it  was  easier  to  grasp  the  individual  parts  as  discrete  units.  Each 
experimenter  used  six  sentences  of  varying  difficulty  so  that  some 
variation  might  be  expected  from  the  selection  of  the  three  sen- 
tences for  the  test.  Whatever  the  cause  of  the  discrepancy  be- 
tween the  results  of  the  two  experimenters,  it  is  obviously 
impossible  to  dbtain  any  reliaible  conclusions  concerning  the  cor- 
relation of  this  ability  with  age,  grade  or  sex,  on  account  of  the 
presence  of  so  many  variable  factors. 

Three  problems  were  used  in  the  test  of  making  change, 
20c  —  4c,  25c  —  6c  and  25c  —  9c,  the  process  of  subtraction 
involved  in  each  being  of  unequal  difficulty.  Certain  variations 
occurred  in  the  tests  of  comparing  remembered  objects  and  com- 
prehending easy  and  difficult  problem  questions.  Alternative 
questions  were  used  in  both  of  these  tests,  and  variations  might 
occur  due  to  the  relative  severity  of  the  experimenters'  judg- 
ments in  marking  the  responses  passed  or  failed.  None  of  the 
tests  in  which  alternative  cjuestions  were  used  will  be  treated  in 
the  subsequent  discussion  of  the  results. 

At  the  close  of  the  experiment,  it  appeared  tliat  a  difference 
of  procedure  had  existed  between  A  and  B  in  the  test  of  indi- 
cating omissions  in  pictures.  A  and  B  both  showed  the  three 
faces  first,  and  the  figure  with  the  arms  missing  last,  according 
to  the  standard  procedure,  but  A,  if  his  subjects  failed  to  detect 
the  parts  omitted  from  the  faces,  would  give  them  another  trial 
after  they  had  detected  the  missing  arms.  A  gave  this  test  to 
51  boys  and  33  girls,  B  to  30  boys  and  30  girls,  his  subjects 
averaging  about  a  year  and  a  half  above  those  of  A.  The  test 
was  passed  by  76%  of  A's  boys  and  97%  of  A's  girls,  but  by 
only  60%  of  B's  boys  and  6^%  of  B's  girls,  showing  that  the 
difference  of  procedure  had  a  most  striking  effect  on  the  results. 
It  is  interesting  to  note  what  the  effect  of  a  difference  of  this 
magnitude  would  mean  if  the  material  from  this  test  were  used 


30  CARL  C.  BRIGHAM 

as  a  basis  of  assigning  it  to  the  proper  ''age  group''  in  the  scale. 
If  a  test  is  to  be  considered  normal  for  a  given  age  if  it  is  passed 
by  75%  of  the  non-selected  school  children  of  that  age,  the  test 
of  indicating  omissions  in  pictures  would  be  a  "six  year"  test 
for  A,  and  an  "eight  year"  test  for  B.  The  data  from  this  test 
will  not  be  treated  in  the  subsequent  discussion. 

In  the  analysis  of  the  results  of  the  definitions  test,  it  was 
found  that  certain  differences  existed  between  A,  B  and  C  in 
scoring  the  responses  of  the  subjects  as  superior  to  use.  No  esti- 
mates could  be  made  concerning  D,  for  he  did  not  record  the 
actual  responses.  B,  C  and  D  gave  this  test  to  approximately 
the  same  range  of  subjects,  averaging  about  9  years.  The  cor- 
rected results  of  B  and  C  show,  in  all,  28%  of  their  subjects 
giving  definitions  superior  to  use,  while  65%  of  D"s  subjects  pass 
this  test.    Obviously  D  was  very  much  more  lenient  than  B  and  C. 

The  influence  of  the  personal  equation  may  or  may  not  be 
present  in  the  remaining  tests.  In  the  opinion  of  the  writer  it 
is  not  present  to  any  marked  degree.  The  data  of  the  four  ex- 
perimenters were  treated  in  several  ways,  and  in  none  of  these 
was  it  possible  to  demonstrate  this  influence.  The  writer's  opin- 
ion, however,  is  more  or  less  certain  according  to  the  test.  The 
tests  of  repeating  digits  might  show  a  slight  difference  between 
C's  results  and  those  of  the  other  experimenters,  a  difference 
which  could  be  explained  by  reference  to  the  rate  at  w^hich  the 
digits  were  spoken.  The  results  of  experimenter  D  are  slightly 
lower  than  those  of  the  other  experimenters  in  the  tests  of 
naming  60  words  in  three  minutes  and  naming  rhymes.  Whether 
these  differences  are  real  or  not,  the  writer  does  not  know.  The 
data  from  these  tests  are  included  in  the  subsequent  study. 

In  the  subsequent  treatment  of  the  results  in  terms  of  grade 
and  sex,  the  material  from  the  following  tests  will  be  treated. 

VI-2  and  IX-2,  Defining  in  terms  of  use  and  in  terms  superior 

to  use. 
VII-i,  Counting  13  pennies. 
VII-2,  Describing  pictures. 
VII-4,  Copying  diamond. 
VII-5,  Naming  four  colors. 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  Zl 

VIII-2,  Counting  backward  from  20  to  o. 

VIII-3,  Enumerating  the  days  of  the  week. 

VIII-4,  Counting  stamps  (three  singles  and  two  doubles). 

VIII-5,  X-3  and  XII-i,  Repeating  5,  6  and  7  digits. 

IX-3,  Naming  the  day  and  date. 

IX-4,  Enumerating  the  months. 

X-i,  Naming  the  pieces  of  money. 

X-2,  Drawing  designs  from  memory. 

X-5  and  XI-2,  Constructing  a  sentence,  containing  one  or  two 

ideas  from  three  given  words. 
XI-3,  Giving  60  words  in  three  minutes. 
XI-4,  Giving  rhymes  with  "day",  "mill"  and  "spring". 

The  treatment  of  the  results  of  the  definitions  test  will  be 
confined  to  the  recorded  and  corrected  definitions  of  A,  B  and  C. 
The  results  from  the  diamond  test  are  based  on  the  scoring  sys- 
tem outlined,  the  passing  mark  being  the  fourth  group  unless 
otherwise  indicated.  The  arbitrary  point  system  of  scoring  the 
design  test  is  used  in  the  subsequent  calculations,  the  passing 
mark,  unless  otherwise  noted,  being  15  points.  The  corrected 
scoring  of  the  sentence  tests  will  be  used. 

The  foregoing  study  of  the  effect  of  the  personal  equation 
shows  conclusively  that  in  certain  tests  this  influence  is  present 
to  a  very  marked  degree.  The  errors  involved  may  be  traced 
to  three  sources,  to  the  apparatus  used,  to  the  technique  of  the 
experimenters  in  giving  the  tests,  and  to  the  experimenter's  ob- 
servation in  marking  the  test  passed  or  failed. 

The  error  due  to  apparatus  may  result  from  a  variation  in  the 
material  itself,  or  from  the  calibration  of  different  sorts  of  ma- 
terial as  equal  in  difficulty,  e.  g. — alternative  questions.  The 
variation  in  the  material  used  by  B  and  C  in  the  test  of  recon- 
structing dissected  sentences  illustrates  the  error  due  to  defect 
in  the  material.  The  writer  has  seen  apparatus  for  the  line  sug- 
gestion test  in  use,  in  which  the  last  three  pairs  of  lines  were 
actually  unequal,  the  difference  between  the  pairs  being  above 
the  threshold  of  discrimination.  The  subject  with  good  dis- 
crimination will  invariably  fail  this  test  when  this  faulty  ap- 
paratus is  used. 

The  error  due  to  the  use  of  alternative  questions  is  more 


Z2  CARL  C.  BRIGHAM 

common  and  therefore  has  more  practical  significance  than  de- 
fects in  the  material  itself.  There  is  a  strong  temptation  for 
an  experimenter,  who  believes  a  certain  question  to  be  unfair, 
to  substitute  another  which  seems  to  him  to  be  of  the  same  diffi- 
culty. In  the  study  of  the  Trenton  results,  which  will  follow, 
it  will  be  shown  that  the  different  questions  included  under  the 
same  test  are  not  of  the  same  difficulty.  The  question,  "What 
would  you  do  if  you  were  delayed  in  going  to  school?"  was 
passed  by  practically  none  of  the  normal  children  of  12,  13  and 
14.  If  this  question  is  changed  to  Goddard's  (28)  interpreta- 
tion, "What  ought  one  to  do  if  he  is  afraid  he'll  be  late  for 
school?",  the  test  is  easily  within  reach  of  the  12  year  children. 
The  difficulty  in  the  first  test  is  caused  by  the  word  "delayed". 
Changing  the  structure  of  the  test  changes  its  nature  completely. 
In  this  connection  it  is  to  be  regretted  that  Town  {y2)  in  the 
appendix  of  her  translation  of  Binet's  191 1  scale,  has  changed 
the  wording  of  some  of  the  tests  from  that  in  the  actual  body 
of  the  translation.  For  example,  the  question  "What  would 
you  do  before  taking  part  in  an  important  afifair?"  (page  47) 
is  changed  to  "Before  taking  part  in  something  very  important, 
what  would  you  do?"  (page  78),  and  "Why  is  a  bad  action 
done  when  one  is  angry,  more  excusable  than  the  same  action 
when  one  is  not  angry?"  (page  47),  becomes  "Why  do  we 
more  easily  pardon  a  bad  act  done  in  anger  than  a  bad  act  done 
without  anger?",  (page  79).  The  meaning  is  the  same  but  the 
wording  different;  and  in  many  cases  success  or  failure  in  a 
test  depends  on  the  interpretation  of  a  single  word.  If  an  ex- 
perimenter using  Town's  translation  were  allowed  to  select  his 
questions  from  the  actual  translation  or  the  appendix  indiscrimi- 
nately, variations  would,  in  all  probability,  result.  The  general 
proposition  that  there  is  no  such  thing  as  an  alternative  question, 
i.  e.  a  question  involving  the  same  mental  processes  and  having 
the  same  difficulty  as  another,  could  very  easily  be  maintained. 
To  avoid  this  error  experimenters  should  adhere  strictly  to  one 
wording  and  should  never  be  allowed  to  substitute  one  question 
for  another. 

An  example  of  the  influence  due  to  differences  of  the  tech- 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  33 

nique  of  the  experimenters  in  giving  the  tests  is  afforded  by  the 
test  of  detecting  omissions  in  pictures.  This  test  is  a  "six  year" 
test  for  A  and  an  "eight  year"  test  for  B.  Differences  in  pro- 
cedure make  it  very  difficult  if  not  impossible  to  compare  the 
results  of  one  investigator  with  those  of  another.  To  eliminate 
this  error,  very  careful  and  minute  instructions  should  be  pub- 
lished for  the  giving  of  each  test.  No  edition  of  the  Binet- 
Simon  scale  is  entirely  satisfactory  in  this  particular. 

Examples  of  errors  due  to  the  observation  of  the  experi- 
menters are  afforded  by  the  tests  of  copying  a  diamond  and 
defining  in  terms  superior  to  use.     Errors  due  to  observation 
may  be  avoided  or  minimized  by  increasing  the  number  of  grades 
of  response  with  which  the  particular  response  in  question  may 
be  compared.    This  principle  is  followed  by  Yerkes  (82)  in  the 
arrangement  of  the  Point  Scale.     In  the  diamond  test,  for  ex- 
ample, Yerkes  allows  three  grades  of  response  while  Binet  al- 
lows but  two — plus  or  minus.     The  accuracy  of  any  measure 
increases  with  the  number  of  gradations  on  the  measuring  scale, 
and  the  significance  of  the  error  of  observation  is  diminished 
by  decreasing  the  chances  of  wide  displacement.     In  the  tests 
in  which  a  definite  question  is  put  to  the  subject,  uniformity  of 
scoring  may  be  obtained  by  an  accurate  and  painstaking  catalogu- 
ing, and  a  subsequent  classification  and  weighting  of  all  the 
responses  of  a  large  number  of  subjects  to  each  question.     If  the 
responses  to  a  free  association  test  may  be  classified  into  a  re- 
latively small  number  of  groups,  then  the  responses  to  a  restricted 
association  test  could  be  classified  into  a  much  smaller  number 
of  groups.     A  sufficiently  large  number  of  responses  will  include 
practically  all  possible  responses.     In  this  way  the  chances  of 
the  error  due  to  observation  are  diminished,  while  the  adoption 
of  a  point  system  of  scoring  will  minimize  the  effect  of  any  errors 
that  might  be  made. 

The  differences  between  the  experimenters  in  this  study  are 
large  enough  to  demonstrate  the  influence  of  the  personal 
equation.  Scientific  procedure  demands  that  the  investigator 
who  studies  the  results  of  the  individual  tests  for  the  purpose  of 
analysing  the  factors  involved  or  for  obtaining  age  norms  should 


34  CARL  C.  BRIGHAM 

demonstrate  that  the  effect  of  the  personal  equation  is  not  present 
in  the  results  treated.  The  burden  of  proof  should  be  on  the 
person  who  maintains  that  the  influence  is  not  present.  Negative 
results  concerning  the  influence  of  the  personal  equation  that 
are  based  on  the  method  of  comparing  the  total  scores  or  "mental 
ages"  of  different  experimenters  should  not  be  taken  as  conclu- 
sive, inasmuch  as  the  experimenters  may  deviate  in  one  direction 
in  one  test,  and  in  the  opposite  direction  in  another,  so  that  in 
a  total  score  these  deviations  might  equalize.  In  a  study  of  this 
sort  made  on  the  basis  of  "mental  ages,"  which  has  previously 
been  reported,  the  writer  (14)  found  no  deviations  between  B. 
C  and  D,  while  deviations  between  these  three  experimenters  do 
appear  in  the  more  detailed  study  of  the  individual  tests.  Studies 
of  the  individual  tests  can  have  no  claim  to  reliability  unless  the 
personal  equation  has  been  eliminated. 

The  importance  of  the  personal  equation  as  a  source  of  error 
in  making  diagnoses  on  the  basis  of  the  "mental  age"  of  the 
subject  is  universally  recognized  by  psychologists  and  almost 
universally  ignored  by  medical  men,  field  workers,  school  teachers 
and  others  who  have  had  no  experience  in  making  mental  meas- 
urements. Among  psychologists  there  are  two  opinions  concern- 
ing the  solution  of  the  difficulty  arising  from  this  source,  the 
first,  that  of  making  certain  allowances  for  the  inexpert  ex- 
aminers or  establishing  limits  within  which  their  opinions  are 
valid,  the  second,  that  of  removing  the  scale  from  their  hands 
entirely. 

Doll  (22)  in  discussing  criticisms  of  the  Binet  scale  on  the 
ground  that  diagnoses  of  normality  and  feeble-mindedness  are 
made  by  inexpert  examiners  urges  "that  those  who  are  capable  of 
doing  good  Binet  testing  of  the  mechanical  sort  without  ibeing 
clinical  psychologists  should  report  the  findings  of  their  examina- 
tions of  children  or  groups  in  tables  of  related  chronological  and 
mental  ages  and  not  in  terms  of  normality  or  abnormality.  In 
their  reports  they  can  say  with  a  high  degree  of  certainty  that 
those  children  who  show  an  intellectual  retardation  of  more  than 
3  years  are  feeble-minded,  but  they  should  not  say  that  those 
wlio  test  less  than  3  years  retarded  are  backward  or  normal.     In 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  35 

the  lesser  degrees  of  retardation  only  the  expert  is  capable  of 
evaluating  the  details  of  a  Binet  test  with  any  finality  as  to  either 
diagnosis  or  prognosis."     (page  607). 

Doll  also  points  out  that  Binet  examiners  who  have  worked  in 
institutions  give  very  reliable  diagnosis,  for  they  intuitively  sense 
distinctions  which  inexpert  laymen  do  not  see.  When  the  re- 
sponsibility for  the  diagnosis  is  placed  on  the  examiner  in  this 
way,  the  scale  it  treated  as  a  qualitative  instrument.  This  stand- 
point is  quite  different  from  that  in  which  certain  allowances  are 
made  for  all  inexpert  examiners  and  the  quantitative  character  of 
the  scale  preserved.  Goddard  (31)  in  a  study  of  the  personal 
equation  based  on  re-testings  of  normal  and  feeble-minded  in- 
dividuals fixes  the  quantitative  limits  somewhat  higher.  "In  all 
cases  where  a  child  tests  four  or  more  years  behind  his  age,  there 
is  little  danger  of  error  in  considering  him  feeble-minded,  even 
though  the  test  was  made  by  a  person  who  was  not  highly  expert, 
provided  such  a  person  is  able  to  use  the  test  with  reasonable 
intelligence.  With  the  borderline  cases,  those  vVho  are  two  or 
three  years  backward,  the  best  expert  should  be  employed  in 
the  testing."    (pages  J^-yy). 

As  early  as  19 10,  before  the  scale  had  received  very  extensive 
application,  Huey  (35)  took  the  stand  that  inexpert  examiners 
sihould  not  use  the  scale.  In  discussing  this  point  he  said,  "I 
w^ould  urge  that  these  Binet  tests  must  be  used  with  judgment 
and  trained  intelligence,  or  they  will  certainly  bring  themselves 
and  their  authors  into  undeserved  disrepute. — Results  can  be  con- 
sidered valid  only  when  the  tests  are  made  by  an  experienced 
psychologist  who  has  familiarized  himself  with  Binet's  directions, 
or  by  other  competent  persons  who  apply  the  tests  under  the 
direction  and  supervision  of  such  a  psychologist."    (page  444). 

Three  years  later,  in  referring  to  the  reports  that  the  medical 
inspectors  in  Pittsburgh  were  to  take  over  the  Binet  testing  in  the 
sichools,  Whipple  (78)  says,  "And  we  can  only  express  our  hopes 
that  these  reports  are  unfounded,  or  that  at  least  those  in  au- 
thority may  be  led  to  understand  that  for  a  person,  whoever  he 
may  be,  without  extensive  psychological  training  to  attempt  to  di- 
agnose the  precise  mental  status  of  a  school  child  is  about  as 


36  CARL  C.  BRIG  HAM 

absurd  as  for  a  mere  psychologist  to  attempt  to  diagnose  in- 
cipient tuberculosis  or  any  other  obscure  pathological  condition." 
(page  302).  The  same  position  is  taken  by  Whipple  {yy)  in 
anbther  editorial.  "We  have  no  quarrel  with  the  use  of  the 
scale  in  the  public  school:  properly  used,  it  is  of  direct  and 
practical  value ;  but  improperly  used,  it  will  become  a  farce  which 
can  but  bring  discredit  upon  psychology  and  retard  the  movement 
for  its  application  to  educational  practise."     (Page  119). 

In  defense  of  this  position,  Whipple  calls  attention  to  an  error 
inherent  in  the  procedure  of  all  inexpert  examiners.  "There  is 
nothing  about  the  conduct  of  the  Binet-Simon  tests  that  is  in- 
trinsically difficult,  yet  there  is  a  source  of  error  inherent  in  the 
use  of  any  psychological  procedure,  which,  as  experience  shows, 
is  surmountable  only  by  drill  in  psychological  experimentation. 
I  refer  to  the  difficulty  of  following  directions.  No  one  who  has 
drilled  students  in  the  laboratory  has  failed  to  be  struck  with  the 
impossibility  of  laying  down  fool-proof  directions  for  the  conduct 
by  an  amateur  of  a  psychological  test."     (Page  119). 

Kuhlmann  (43)  agrees  with  Whipple  in  this  position.  "The 
untrained  examiner  meets  difficulties  because  he  lacks  the  follow- 
ing: (a)  Familiarity  with  the  directions  for  giving  the  tests, 
(b)  Familiarity  with  the  rules  for  interpreting  the  responses  of 
the  children,  (c)  Ability  to  adapt  the  procedure  in  testing  in 
special  instances  for  which  directions  can  not  be  given,  (d) 
Ability  to  interpret  responses  in  special  instances  for  w'hich 
rules  can  not  be  given,  (e)  Ability  to  adapt  himself  in  attitude 
to  the  mental  levels  of  children  of  different  ages  so  as  to  obtain 
the  best  efforts  from  the  child  in  each  case,  (f)  General  ap- 
preciation of  the  absolute  necessity  of  adhering  strictly  to  all 
rules  of  testing,  and  of  careful,  painstaking  work.  These 
deficiencies  are  of  quite  different  degrees  of  importance.  The 
last  is,  on  the  whole,  the  most  serious  and  most  frequent,  and 
can  be  remedied  only  by  extended  laboratory  training."  (Pp.  255 
and  256).  In  regard  to  the  quantitative  allowance  that  must  be 
made  for  inexpert  examiners,  Kuhlmann's  article  affords  the 
following,  "The  amount  of  error  made  by  an  examiner  because 
of  his  lack  of  training  seldom  equals  two  years  in  the  mental 
age;  in  the  majority  of  cases  it  is  less  than  one  year."  (Page  256). 


IV.     GRADE  CORRELATIONS 

The  correlation  between  intelligence,  as  measured  by  the  Binet 
scale,  and  school  performance,  as  measured  by  age  and  grade 
standing,  has  been  worked  out  by  various  investigators.  In  all 
cases  intelligence  was  measured  by  the  "mental  age"  or  total 
score  of  the  Binet  tests,  and  pedagogical  age  by  assuming  that  all 
children  begin  school  at  a  certain  age  and  should  therefore  be  in 
certain  grades  at  certain  ages.  Stem  (62)  has  reviewed  the 
work  of  Goddard  (30),  Binet  (4),  and  Bobertag  (10)  in  this 
field,  with  the  general  conclusion  that  the  correlation  is  only 
moderately  high.  The  number  of  children  showing  mental 
advance  is  in  excess  of  those  showing  pedagogical  advance,  but 
very  rarely  do  children  showing  pedagogical  retardation  show 
mental  advance.  The  correlation  is  one-sided  in  that  "inference 
from  school  performance  to  mental  ability  is  safer-  than  from 
mental  ability  to  school  performance."  (Page  61).  Stern  ac- 
counts for  the  discrepancies  on  the  ground  that  "performance 
in  the  school  depends  not  only  upon  intelligence,  but  also  upon 
certain  other  and  quite  different  factors."  (Page  63).  These 
factors  are  strength  of  memory  which  plays  a  large  part  in 
school  performance  but  correlates  only  to  a  moderate  degree 
with  intelligence,  and  other  factors  that  have  nothing  to  do  with 
intellect  but  belong  largely  in  the  domain  of  the  will — "the 
degree  and  duration  of  attention,  industry  and  conscientiousness, 
sense  of  duty  and  capacity  to  fit  into  the  social  group."  (Page  63). 
Stern  concludes  that  "the  lack  of  agreement  between  tests  of  in- 
telligence and  school  perfonnance  is  really  calculated  to  increase 
our  confidence  in  the  psychological  test-methods,"  (Page  64) 
that  absolute  correlation  is  not  to  be  desired  since  that  w^ould 
mean  that  the  tests  were  testing  school  performance  only,  and 
that  the  measure  of  intellectual  ability  was  the  school  performance 
itself,  the  tests  being  superfluous. 

More  recently,  Schmitt  (57)  has  reviewed  the  work  of  God- 


38  CARL  C.  BRIGHAM 

dard,  Terman  and  Childs  (66)  and  Dougherty  (23)  in  corre- 
lating intelligence,  as  measured  by  the  Binet  scale,  and  school 
performance,  and  reaches  conclusions  quite  opposite  to  those  of 
Stern,  The  following  quotations  from  Schmitt's  monograph  ex- 
plain her  view  point.  "Further  doubt  is  cast  upon  the  accuracy 
of  the  tests  by  the  fact  that  judgments  arrived  at  through  their 
application  do  not  coincide  with  that  of  the  school  concerning  the 
same  subjects."  (Page  57).  Concerning  this  lack  of  correlation 
Schmitt  writes  "The  Binet  tests,  therefore,  while  professing  to 
test  native  ability  are  concerned  very  little  with  the  education 
which  all  normal  children  have  the  native  ability  to  acquire, 
and  which  is  of  much  importance  in  civilized  life."  (Page  60). 
To  the  investigations  cited  Schmitt  has  added  one  of  her  own, 
in  whic'h  the  lack  of  correspondence  between  the  Binet  "mental 
age"  and  school  grade  is  shown. 

The  writer  is  of  the  opinion  that  the  method  of  correlating 
school  performance  with  "mental  age"  fails  to  demonstrate  either 
the  adequacy  of  the  Binet  tests  according  to  Stern,  or  the  com- 
plete inadequacy  of  the  tests  according  to  Schmitt.  For  the 
demonstration  of  this  point  Schmitt's  investigation  may  be  dis- 
cussed, inasmuch  as  it  shows  the  most  striking  deviations  between 
the  measures  of  the  two  performances.  Schmitt  applied  Binet's 
191 1  scale  (Town's  translations  with  modifications)  to  150 
children  of  superior  social  status.  The  following  quotations  in- 
dicate the  status  of  the  subjects.  "The  children  who  served  as 
subjects  for  the  tests  comprised  the  Kindergarten  and  first  six 
grades  of  a  private  school  in  Chicago."  "They  were  the  chil- 
dren of  the  professional  class  mainly.  A  few  were  children  of 
successful  business  men  w^ho  sought  the  best  obtainable  type  of 
education  for  their  children."  (Page  2).  The  tests  were  ap- 
plied at  the  close  of  an  examination  with  the  Healy-Fernald  tests 
tmder  rather  unfavorable  conditions  as  indicated  by  the  follow- 
ing quotations, — "In  the  conduct  of  the  two  sets  of  tests  the 
Binet-Simon  tests  were  reserved  for  the  last.  By  the  time  they 
were  reached  the  child  had  been  doing  tests  for  an  hour  or  more. 
In  some  cases  there  was  too  much  restlessness  and  fatigue  to 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  39 

carry  the  child  as  far  as  the  majority  of  his  comrades  in  his 
grade  were  able  to  go  and  the  tests  were  then  discontinued." 
(Page  68  and  69). 

The  tests  in  the  various  age  groups  given  to  each  grade  were 
as  follows, — Kindergarten,  tests  for  V,  VI,  VII,  VIII  and  IX 
years;  Grade  I,  tests  for  V,  VI,  VII,  VIII,  IX,  X  and  XII  years; 
Grade  II,  tests  for  VI,  VII,  VIII,  IX,  X,  and  XII  years.  Grades 
III  and  IV,  tests  for  VIII,  IX,  X  and  XII  years ;  Grade  V,  tests 
for  IX,  X,  XII  and  XV  years;  Grade  VI,  tests  for  XII  and  XV 
years.  The  "Adult"'  tests  were  also  given  to  Grade  VI  as  a 
class-room  test. 

Schmitt  compared  three  measures,  chronological  age,  school 
grade  age  and  "mental  age".  The  "mental  age",  in  case  a  sub- 
ject passed  all  tests  in  one  group  and  failed  one  or  more  in  a 
lower  group,  could  be  reckoned  from  two  basal  ages,  these 
alternative  rating  being  included  by  Schmitt.  The  summary  of 
the  results  is  as  follows, —  Comparing  the  Binet  age  to  the 
chronological  age,  14  (or  20)%  are  retarded,  26  (or  24)%  are 
normal,  and  58  (or  54)%  are  advanced.  Comparing  the  school 
grade  to  the  chronological  age,  (using  5  to  6.5  years  as  the  nor- 
mal age  for  the  Kindergarten,  6.5  to  7.5  for  Grade  I  etc.)  38% 
are  retarded,  56%  are  normal  and  4%  are  advanced.  Comparing 
the  Binet  age  to  the  school  grade  age,  2  (or  4)%  are  retarded, 
-5  (or  35)%  are  normal  and  y2  (or  60)%  are  advanced.  The 
essential  discrepancies  are  indicated  by  Schmitt  by  the  follow- 
ing,'—  "Where  the  school  grading  shows  4%  advanced  over  the 
normal  for  the  chronological  age,  the  Binet  grading  shows  58% 
over  the  chronological  age  and  y2%  over  the  age  normal  to  the 
school  grade."  (Page  80.)  The  discrepancies  thus  indicated, 
although  much  larger  than  those  of  other  investigators,  agree 
with  the  general  trend  of  results  in  that  more  children  are  shown 
to  be  advanced  according  to  the  Binet  mental  age  than  according 
to  the  school  grade  age.  The  results  disagree  with  those  of 
other  investigators  in  finding  a  higher  per  cent,  advanced  by 
Binet  age  compared  to  chronological  age. 

The  inadequacy  of  the  methods  employed  in  the  investigations 
of  Schmitt  and  others  is  seen  when  the  measures  are  separately 


40  CARL  C.  BRIGHAM 

Studied.  The  use  of  the  normal  grade  age  as  a  measure  of 
scholastic  ability  is  false  inasmuch  as  it  rests  on  the  assumption 
that  all  children  enter  school  at  a  certain  age,  which  is  not  the 
case.  The  measure  of  scholastic  ability  is  the  measure  of  the 
child's  reaction  to  the  subject  matter  of  the  grades,  and  that 
measure  may  be  expressed  only  in  the  fact  of  promotion,  non- 
promotion  or  (very  rarely)  double  promotion,  in  other  words, 
it  may  be  expressed  only  in  the  relation  of  grade  to  the  length 
of  time  in  school.  Furthermore,  the  two  measures  of  scholastic 
ability,  the  age  in  grade  method,  and  the  grade  progress  method, 
are  measures  of  an  historically  past  performance  not  of  present 
possibilities,  and  the  true  measure  of  an  ability  must  indicate 
potential  ability. 

As  measures  of  scholastic  ability  in  terms  of  actual  reaction, 
these  measures  present  a  distribution  of  general  ability  that  is 
skewed  toward  the  lower  end,  or  in  the  direction  of  no  ability. 
If  a  child  enters  school  late,  he  presents  a  picture  of  retardation 
according  to  the  age  and  grade  method,  while  throug^h  any  num- 
ber of  causes  independent  of  intellectual  ability,  a  child  may 
present  a  retardation  of  at  least  a  year  according  to  either  method. 
The  possibilities  for  advancement  are  not  as  great,  however,  for 
advancement  means  forcing  a  child  through  a  mass  of  subject 
matter,  a  process  which  the  school  is  generally  unwilling  to 
undertake  and  the  parent  is  generally  unwilling  to  sanction.  The 
school  therefore  presents  a  picture  of  ability  in  which  promotion 
is  normal,  and  non-promotion  far  more  frequent  than  advance. 
If  general  ability  is  to  be  considered  as  distributed  over  any  sort 
of  a  frequency  surface,  that  surface  will  not  take  the  form 
presented  by  the  school  measure  in  which  the  modal  ability  is 
almost  completely  the  upper  limit. 

The  measure  of  "mental  age"  has  been  shown  to  be  one  which 
varies  from  one  chronological  age  to  another  in  the  form  of  its 
distribution.  Normal  children  of  6  or  7  test  over  age,  while 
those  of  II  and  12  test  under  age.  This  abnormal  distribution 
is  due  to  two  facts.  In  the  first  place,  the  tests  in  the  younger 
years  are  too  easy  and  those  in  the  higher  years  are  too  difficult. 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  41 

In  the  second  place,  the  younger  children  have  a  wider  range 
of  tests  beyond  their  average  abihty,  so  that  exceptional  sub- 
jects may  display  exceptional  ability  in  a  manner  that  is  im- 
possible if  ability  is  measured  by  school  progress,  while  older 
children  have  only  a  few  tests  within  their  range,  the  picture 
of  advancement  being  excluded  as  in  the  measure  of  school 
ability.  If  the  mental  ages  of  a  run  of  subjects  of  different 
chronological  ages  are  combined,  the  frequency  surface  is  nor- 
mal, the  error  of  the  extremities  balancing. 

The  investigators  who  have  compared  ''mental  age"  with  grade 
age,  have  compared  two  distributions,  one  of  which  is  markedly 
skewed,  the  other  normal,  but  false.  The  resulting  finding  of 
mental  advance  in  excess  of  pedagogical  advance  has  significance 
only  insofar  as  it  shows  that  a  measure  of  general  ability  that 
will  admit  of  exceptionally  high  performance  is  a  better  measure 
than  one  that  precludes  the  possibility  of  such  performance.  The 
only  significant  finding  is  that  pupils  who  show  marked  retarda- 
tion in  school  rarely  if  ever  show  mental  advance. 

Applying  the  foregoing  discussion  to  Schmitt's  results  in  par- 
ticular, all  that  has  been  said  concerning  the  inadequacy  of  the 
age  in  grade  method  applies  to  her  results.  The  age  for  enter- 
ing school  being  5,  none  of  the  subjects  in  the  Kindergarten  could 
be  advanced,  w^hile  those  wdio  entered  late  would  be  retarded. 
It  is  difficult  to  see  how  these  young  children  would  be  able  to 
make  up  their  work  in  such  a  way  as  to  show  advance  during  the 
first  two  or  three  school  years.  The  normal  age  for  the  sixth 
grade  is  from  11.5  to  12.5  years.  Inasmuch  as  no  grades  were 
tested  above  VI,  none  of  the  37  subjects  from  11,5  to  14.5  could 
show  an  advance,  and  all  of  the  19  subjects  from  12.5  to  14.5 
would  necessarily  show  retardation.  Schmitt's  results  differ 
from  those  of  other  investigators  in  finding  more  subjects  ad- 
vanced according  to  Binet  age  in  relation  to  chronological  age. 
This  deviation  is  probably  due  to  the  fact  that  she  examined  a 
superior  selection  of  subjects,  and  to  the  fact  that  the  XV  year 
and  "Adult"  tests  were  used,  so  that  the  older  subjects,  who  in 
general  fall  below  their  chronological  age,  had  an  opportunity  to 


42  CARL  C.  BRIGHAM 

better  their  scores.  The  discrepancy  shown  by  Schmitt  between 
school  standing  and  the  Binet  tests  does  not  demonstrate  the 
inadequacy  of  the  tests. 

The  final  demonstration  of  a  correlation  between  the  Binet 
scale  and  school  grade,  rests  not  in  comparing  the  total  score  or 
"mental  age"  with  school  grade,  for  that  is  susceptible  to  the 
errors  of  over-estimation  and  under-estimation  according  to  vary- 
ing chronological  age,  but  in  comparing  the  results  of  subjects 
in  each  grade  on  the  individual  tests.  The  tests  may  vary  in 
their  correlation  with  grade.  Inasmuch  as  there  is  a  general 
growth  in  age  with  grade,  and  a  corresponding  growth  of  in- 
telligence with  age,  a  test,  in  order  to  be  an  adequate  test  of 
intelligence,  must  show  a  correlation  with  grade.  If  the  correla- 
tion is  too  high,  however,  the  value  of  the  individual  test  is  in 
question  for  it  would  then  be  testing,  not  intelligence,  but  grade 
training.  This  criterion  was  actually  used,  though  not  stated, 
by  Binet  in  his  discussion  of  the  results  of  Decroly  and  Degand 
(19),  and  in  his  revision  of  the  1908  scale,  in  which  many  of 
the  tests  that  he  considered  to  relate  to  school  training  were 
eliminated. 

Studies  of  the  individual  tests  in  the  light  of  school  grade  are 
not  available.  Decroly  and  Degand  published  in  1910  the  re- 
sults of  an  investigation  on  45  children  in  a  Brussels  school, 
similar  in  character  to  that  studied  by  Schmitt  in  Chicago.  Binet 
discussed  these  results  and  those  of  other  minor  investigations  in 
the  Paris  schools  in  considering  the  effect  of  environment  on 
the  results  of  the  tests.  Although  he  referred  to  school  training 
as  a  factor,  and  classified  the  tests  in  which  Decroly  and  Degand's 
subjects  were  superior,  he  gave  no  quantitative  demonstration  of 
the  effect  of  this  factor.  The  results  of  Decroly  and  Degand 
are  based  on  too  few  subjects  to  admit  of  quantitative  treatment. 
Chotzen  (18)  studied  the  tests  by  comparing  the  performance  of 
feeble-minded  individuals  of  the  same  mental  age  but.  of  different 
chronological  age.  Although  this  method  shows  the  effect  of 
environment  and  maturity  on  feeble-minded  individuals,  it  does 
not  bear  directly  on  the  factor  of  school  training.     The  foregoing 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  43 

investigations  will  be  discussed  in  this  chapter  only  in  their 
relation  to  the  results  of  the  particular  tests.  Schmitt,  in  her 
monograph,  published  tables  showing  the  reaction  of  each  sub- 
ject in  each  grade  to  each  test,  the  tables  being  discussed  in  the 
text.  Although  it  was  not  Schmitt's  purpose  to  determine  the 
correlations  between  the  various  tests  and  grade,  her  data  are 
available  for  a  study  of  this  sort,  and  the  writer  has  taken  the 
liberty  of  figuring  them  in  this  light,  indicating  at  the  same  time 
Schmitt's  interpretation  of  the  grade  factor,  contained  in  the 
accompanying  text.  These  data  will  be  compared  with  the  re- 
sults of  the  Princeton  investigation. 

422  subjects  of  this  investigation  were  distributed  in  the 
kindergarten,  first  six  regular  grades,  minus  grades  and  the 
special  class  of  the  Princeton  Model  School.  301  of  the  subjects 
(161  boys  and  140  girls)  were  in  the  kindergarten  and  first  six 
regular  grades.  The  data  obtained  from  the  examination  of 
these  301  subjects  were  classified  according  to  the  grade  in  which 
the  subjects  were  found,  and  the  percentage  that  the  subjects 
of  each  grade  passed  each  test  was  calculated. 

Only  those  tests  were  studied  which  showed  themselves  to  be 
free  from  the  influence  of  the  personal  equation  of  the  four  ex- 
perimenters. The  elimination  of  the  unrecorded  results  of  the 
definitions  test  left  a  number  of  cases  too  small  to  be  studied.  To 
avoid  the  influence  of  the  error  due  to  incomplete  data,  the 
writer  has  calculated  the  percentage  from  only  those  tests  that 
were  given  from  75%  to  100%  of  the  possible  number  of  times. 
The  data  from  the  tests  of  repeating  5,  6  and  7  digits  have  been 
combined  into  one  weig'hted  measure.  The  procedure  of  the 
experimenters  in  giving  these  tests  was  to  start  within  the  sub- 
ject's range  and  continue  till  he  failed.  If  5  digits  were  suc- 
cessfully repeated,  6  were  given,  and  if  these  were  passed,  7  were 
given.  The  results  have  been  combined  into  one  measure  for  the 
sake  of  simplicity,  i  point  being  allowed  for  the  successful 
repetition  of  5  digits,  2  points  for  6  digits  and  3  points  for  7 
digits,  the  weighting  being  roughly  in  accordance  with  the 
weighting  in  Goddard's  scale,  the  tests  being  in  the  age  groups 


44  CARL  C.  BRIGHAM 

VIII,  X  and  XII  respectively.  The  measure  of  the  ability  of  a 
group  to  repeat  digits  is  the  per  cent,  that  the.  number  of  points 
scored  is  of  the  number  of  points  possible  (i.e.  6  times  the  num- 
ber of  subjects  in  the  group). 

The  number  of  subjects  in  each  grade  (boys  and  girls  shown 
separately)  the  average  age  of  the  subjects  in  each  grade,  to- 
gether with  the  mean  variation  from  the  average  are  shown  in 
Table  3. 

TABLE  3 

Number  of  Boys  and  Girls  in  Each  Grade,  and  the  Average  Age  of  All 

Subjects  in  Each  Grade. 

Number        Number  Total  No.       Average  Mean 

Grade              of  Boys        of  Girls  of  Subjects          Age  Variation 

Kindergarten 20                   12  32             5.64  years  0.46  years 

Grade  1 27                  24  51             70s    "  0.50    " 

Grade  II 16                  24  40             8.16    "  0.65    " 

Grade  III 21                   24  45             9-3i     "  0.75    " 

Grade  IV 20                   15  35            10.46    ""  0.91     " 

Grade  V 24                  25  49            11.71     "  0.99    " 

Grade  VI 33                   16  49            12.81     "  1.06    " 

The  above  table  shows  an  increase  of  a  year  or  more  (actually 
from  1. 10  years  to  1.41  years)  in  the  average  age  of  the  subjects 
in  each  grade.  From  this  it  is  reasonable  to  expect  that  there  is 
a  general  growth  in  intelligence  correlating  with  this  increase  in 
age,  or,  in  other  words,  to  expect  a  correlation  between  the  re- 
sults of  the  individual  tests  and  the  grade  in  which  the  per- 
formance occurred.  If  the  correlation  is  too  high,  it  will  in- 
dicate a  dependence  of  that  particular  test  on  the  subject  matter  of 
the  grade.  In  Table  4  are  shown  the  percentages  that  the  sub- 
jects in  each  grade  passed  each  test.  The  notes  referred  to  in 
the  margin  contain  the  proportions  passed  for  all  other  subjects 
for  whom  the  percentages  are  not  given,  the  percentages  being 
given  only  for  those  groups  to  whom  the  tests  were  given  from 
75%  to  100%  of  the  possible  number  of  tirries. 

A  study  of  Table  4  shows  that  the  tests  in  general  correlate 
with  grade.  The  combined  score  of  the  test  of  repeating  digits, 
for  example,  shows  a  growth  from  6%  to  78%,  more  rapid 
in  the  first  three  grades  than  in  the  last  four.     The  tests  vary  in 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  45 

TABLE  4 

Percentage  that  Subjects  in  Each  Grade  Passed  Each  Test.    301  Subjects. 

Grades 

Test                                       K  I          II  III      IV        V       VI 

VII-i,  13  pennies   72  96      100  Note    i 

VII-2,  Pictures  69  96        94  Note    2 

VII-4,  Diamond  46  75        88  Note    3 

VII-5,  Colors  72  90        97  Note     i 

Vni-2,  20  to  0   9        53  80                                    Note    4 

VIII-4,  Stamps    13        50  78                                    Note    5 

All  digits,   (combined) 6  21        42  51         55        78        75 

VIII-3,  Days  of  week 16  45        90  100                                     Note    6 

IX-3,  Date   5        35  96      100                          Note    7 

IX-4,  Months  28  84        90                          Note    8 

X-I,  Money  20  2,6        57        82               Note    9 

X-2,  Designs  21        37        42        66    Note  10 

X-s,  Sentence   (2  ideas)..  67       89       88       98    Note  11 

XI-2,  Sentence  (i  idea)...-  22        46        51        74    Note  12 

XI-3,  60  words   62        6i        87    Note  13 

XI-4,  Rhymes   67        63        76    Note  14 

Note     I.  Counting  13  pennies  and  naming  colors  given  20  times  above  II. 

Not  failed. 
Note    2.  Describing  pictures  given  21  times  above  II.     Not  failed. 
Note    3.  Copying  diamond  given  25  times  above  II.     Not  failed. 
Note    4.  Counting  from  20  to  o  given  18  times  in  K.     Not  passed.     Given 

31  times  above  III.     Failed  once. 
Note    5.  Counting  stamps  given  15  times  in  K.     Not  passed.    Given  35  times 

above  III.    Failed  3  times. 
Note    6.  Naming  days  of  week.    Given  2i2  times  above  III.    Not  failed. 
Note    7.  Giving  day  and  date  given  5  times  in  K.     Not  passed.     Given  56 

times  above  IV.     Not  failed. 
Note    8.  Naming  months.     Given  26  times  below  II.     Passed  twice.     Given 

44  times  above  IV.     Failed  twice. 
Note    9.  Naming  money.    Given  26  times  below  II.    Passed  3  times.    Given 

28  times  in  VI.    Failed  twice. 
Note  10.  Copying  designs  given  33  times  below  III.     Passed  5  times. 
Note  II.  Sentence  (2  ideas)  given  32  times  below  III.    Passed  12  times. 
Note  12.  Sentence  (i  idea)  given  2i2  times  below  III.     Passed  4  times. 
Note  13.  Giving  60  words  given  53  times  below  IV.    Passed  19  times. 
Note  14.  Giving  rhymes  given  42  times  below  IV.     Passed  26  times. 

the  number  of  grades  taken  to  reach  their  maximum.  The  test 
of  naming  the  day  and  date,  for  example,  is  failed  by  all  subjects 
in  the  kindergarten,  95%  of  Grade  I  and  65%  of  Grade  II,  while 
only  4%  of  the  subjects  in  Grade  III  and  none  of  those  in  t-he 


46  CARL  C.  BRIGHAM 

higher  grades  fail  it.  A  sudden  increase  occurs  between  Grades 
II  and  III  showing  possibly  the  influence  of  grade  training.  The 
tests  vary  considerably  in  the  degree  of  their  correlation.  An 
easily  obtained  measure  of  the  degree  of  correlation  is  that  of 
comparing  the  magnitude  of  the  increases  from  grade  to  grade. 
For  example,  there  is  an  increase  of  6i%  (96% — 35%)  from 
Grade  II  to  Grade  III  in  the  ability  to  pass  the  test  of  giving  the 
day  and  date,  and  an  increase  of  16%  (36 — 20%)  between  the 
same  grades  in  the  test  of  naming  the  pieces  of  money.  The 
former  test  correlates  higher  with  the  influence  of  grade  in  this 
particular  case  than  the  latter. 

In  this  manner  the  percentage  difference  between  the  per- 
formance of  the  subjects  in  each  grade  and  that  of  the  subjects 
in  the  preceding  grade  was  obtained.  All  the  increases  or  de- 
creases in  ability  from  one  grade  to  another  were  thus  obtained, 
these  values  serving  as  measures  of  the  amount  of  correlation 
between  the  tests  and  the  grades.  42  differences  between  the 
performance  of  the  subjects  in  any  grade  and  those  of  the  next 
succeeding  grade  were  thus  obtained.  In  4  cases  there  were 
actual  decreases  of  i,  2,  3  and  4%  which  were  not  significant.  The 
difference  ranged  from  — 4%  to  +61%,  the  median  being 
+  19-5%  ( 0=16.25%).  Some  of  the  differences  between  the 
grades  might  be  due  to  the  chance  superiority  of  a  particular 
grade.  To  overcome  this  chance  variation,  and  to  furnish  an- 
other index  of  the  growth  of  the  various  abilities,  the  differences 
were  calculated  by  steps  of  two  grades,  i.e.,  siibtracting  the  per- 
formance of  the  kindergarten  from  the  second  grade,  the  first 
from  the  third,  etc.  In  this  way,  26  differences  were  obtained 
varying  from  -]-g%  to  -\-gi%,  the  median  being  +29% 
(Q=i8%). 

Some  of  the  differences  noted  are  undoubtedly  high  enough  to 
warrant  the  assumption  of  the  effect  of  grade  training  on  the 
tests.  Just  what  tests  show  this  effect  is  probably  a  matter  of  opin- 
ion. Allowance  must  be  made  for  the  growth  of  an  ability 
independent  of  training.  25%  of  the  highest  increases  from 
one  grade  to  another  were  selected  as  being  worthy  of  special 
consideration  at  least.     A  larger  increase  must  be  allowed  be- 


VARIABLE  FACTORS  IN  THE  BINET  TESTS 


47 


tween  two  grades.  Those  differences  were  considered  worthy 
of  special  consideration  that  exceeded  twice  the  vakie  of  the 
median  of  the  one-grade  differences  or  39%.  This  manner  of 
selecting  the  largest  differences  is  quite  arbitrary,  but  is  justified 
by  the  outcome,  for  the  tests  that  show  the  most  significant  in- 
-  -eases  nccording  to  this  method  show  those  increases  in  more 
than  one  step,  so  that  the  evidence  is  concentrated  against  a  very 
few  tests.  In  this  way  the  significant  values  outweigh  the  less 
significant  values  and  fair  allowance  is  made  for  growth  from 
one  grade  to  another. 

The  following  list  includes  the  tests  showing  the  greatest  in- 
creases by  one-grade  and  two-grade  steps,  together  with  the 
magnitude  of  the  increases  and  the  grades  between  which  they 
occur. 


One-grade  steps. 

25%  of  largest 

increases. 

-t-6i%  Date,  II  to  III 

+56%  Months,  II  to  III 

-t-45%  Days,  I  to  II 
-f  44%  20  to  0,  I  to  II 

-1-37%  Stamps,  I  to  II 
4-30%  Date,  I  to  II 

4-29%  Diamond,  K  to  I 
-f29%  Days,  K  to  I 
-f28%  Stamps,  II  to  III 
-1-27%  20  to  o,  II  to  III 
-f-27%  Pictures,  K  to  I 


Two-grade   steps. 

Increases  greater 

than  39%. 

-f-91%  Date,  I  to  III 

-1-74%  Days,  K  to  II 
-\-7i%  20  to  0,  I  to  III 

-1-65%  Stamps,  I  to  III 
-1-65%  Date,  II  to  IV 
-1-62%  Months,  II  to  IV 

-f55%  Days,  I  to  III 

+46%  Money,  III  to  IV 
-f42%  Diamond,  K  to  II 


The  above  lists  of  increases  are  confine'd  to  but  8  tests.  In 
all,  there  were  16  tests  studied.  According  to  the  method  of 
selecting  the  significant  increases,  20  such  values  actually  ap- 
peared. In  this  manner  the  evidence  combines  against  a  very 
few  tests.  Some  tests  appear  in  both  lists  and  more  than  once 
in  the  same  list.  The  most  striking  growth  with  grade  is  shown 
in  the  tests  of  giving  the  day  and  date,  naming  the  months,  nam- 


48  CARL  C.  BRIGHAM 

ing  the  days  of  the  week,  counting  from  20  to  o  and  counting 
stamps.  The  tests  of  copying  the  diamond,  describing  pictures 
and  naming  money  may  or  may  not  show  this  influence.  The 
evidence  is  strongest  in  the  case  of  the  diamond  test  since  that 
appears  in  both  Hsts. 

The  foregoing  method  of  selecting  those  tests  which  correlate 
with  grade  to  such  an  extent  as  to  indicate  the  influence  of  grade 
training  is  not  conclusive,  owing  to  the  fact  that  there  is  also 
an  increase  in  age  from  grade  to  grade.  If  a  test  showed  a 
very  rapid  growth  with  age,  and  those  ages  fell  for  the  most  part 
in  certain  grades,  then  those  grades  would  show  an  increase  which 
might  be  wrongly  assumed  to  be  due  to  training.  The  tests  of 
counting  from  20  to  o  is  a  case  in  point.  Yerkes  (82)  in  Table 
32,  page  125,  gives  the  percentage  values  for  each  test  in  the 
Point  Scale,  for  English  speaking  boys  and  girls  of  each  age. 
The  test,  of  the  twenty  one  tests  included,  that  shows  the  most 
marked  increase  with  age  is  that  of  counting  backward,  the 
values  being  as  follows, —  age  4=0%;  age  5=3.5%;  age 
6=23.7%;  age  7=45.7%;  age  8=72.2%;  age  9=96%;  the 
values  for  ages  above  9  being  97%  or  higher. 

The  age  in  grade  distribution  of  the  301  subjects  in  this  in- 
vestigation is  given  in  Table  5. 

TABLE  s 
Distribution  of  Subjects  in  Each  Grade  according  to  Chronological  Age. 

Grades 


Age 

K 

I 

II 

III 

IV 

V 

VI 

Total 

4 

4 

4 

5 

17 

17 

6 

II 

28 

2 

41 

7 

18 

17 

2 

I 

38 

8 

4 

15 

18 

I 

38 

9 

5 

13 

II 

29 

10 

I 

ID 

14 

18 

I 

44 

II 

I 

2 

3 

l6 

16 

38 

12 

5 

8 

II 

24 

13 

"■ 

4 

12 

16 

14 

2 

5 

7 

15 

I 

3 

4 

16 

I 

I 

Total 

32 

51 

40 

45 

35 

49 

49 

301 

VARIABLE  FACTORS  IN  THE  BINET  TESTS  49 

The  rapid  growth  of  the  abiHty  in  counting  from  20  to  o, 
according  to  the  method  of  comparing  the  subjects  in  each  grade, 
was  from  9%  in  Grade  I  to  80%  in  Grade  III.  From  Table  5 
it  may  be  seen  that  practically  all,  (89%),  of  the  chronolog- 
ical ages  in  Grades  I,  II  and  III  were  distributed  in  the  ages 
6,  7,  8  and  9,  a  chronological  range  coinciding  with  that  in  which 
Yerkes'  results  show  the  ability  to  develop.  The  growth  of 
this  ability  might  be  due  then  either  to  age  or  to  grade.  For 
this  reason,  to  arrive  at  any  final  conclusion,  it  is  necessary  to 
compare  the  subjects  of  the  same  age  but  in  different  grades. 
The  treatment  of  the  Princeton  results  according  to  this  method 
follows,  but  the  analysis  of  the  data  in  this  manner  can  have 
no  great  reliability  owing  to  the  small  number  of  subjects  in  each 
group.  The  number  of  subjects  in  each  group,  (boys  and  girls 
shown  separately),  the  average  age  and  mean  variation  from  this 
average  are  shown  in  Table  6. 

TABLE  6 

Number  of  Boys  and  Girls  of  Similar  Ages  in  Different  Grades,  and  the 

Average  Age  of  the  Subjects  of  Similar  Ages  in  Each  Grade. 

Number    Number      Total  no.     Average  Mean 

Grade  Age         of  Boys      of  Girls    of  Subjects      Age  Variation 

Kindergarten.     5  11  6  17  5-48  0.20 

Kindergarten.     6  8  3  11  6^  0.21 

Grade  I   6  14  M  28  6.59  0.17 

Grade  I  7  9  9  18  7-36  0.22 

Grade  II  7  7  10  17  7.56  0.24 

Grade  II  ....    8  6  9  i5  8.39  0.24 

Grade  III  ...    8  8  10  18  8.60  0.22 

Grade  III  ...     9  5  8  13  9.43  0.16 

Grade  IV  ....    9  5  6  n  9.65  0.13 

Grade  IV  ....   10  10  4  14  10.39  0.30 

Grade  V  10  7  u  18  10.54  0.25 

Grade  V  11  10  6  16  11.54  0.22 

Grade  VI  ...  11  10  6  16  11.53  0.26 

Grade  VI  ....  12  6  5  "  12.52  0.14 

All  chronological  ages  were  computed  in  tenths  of  a  year,  so 
that  a  variation  in  age  from  o.i  yr.  to  0.9  yr.  is  possible  within 


so  CARL  C.  BRIGHAM 


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VARIABLE  FACTORS  IN  THE  BINET  TESTS  Si 

Note    I.  Tests  of  counting  13  pennies,  describing  pictures  and  naming  colors 

each  given  12  times  above  II-8.     No  failures. 
Note    2.  Copying  diamond  given  15  times  above  II-8.    No  failures. 
Note    3.  Counting  from  20  to  o  given  16  times  below  1-6.    Not  passed.    Given 

31  times  above  III-8.    Failed  4  times. 
Note    4.  Counting  stamps  given  14  times  below  1-6.    Not  passed.    Given  32 

times  above  III-8.    Failed  4  times. 
Note    5.  Giving  days  of  week  given  32  times  above  III-8.    No  failures. 
Note    6.  Giving  date  given  39  times  below  II-7.     Passed  twice.     Given  36 

times  above  IV-io.    No  failures. 
Note    7.  Naming  months  given  24  times  below  II-7.     Passed  twice.     Given 

S7  times  above  IV-9.    Failed  4  times. 
Note    8.  Naming  pieces  of  money  given  35  times  below  II-8.    Passed  4  times. 

Given  14  times  above  V-ii.    Failed  twice. 
Note    9.  Copying  designs  given  26  times  below  III-8.    Passed  5  times.    Given 

15  times  above  V-ii.    Failed  6  times. 
Note  10.  Three  words  in  sentence,  2  ideas,  given  24  times  below  III-8.  Passed 

9  times. 
Note  II.  Sentence,  i  idea,  given  same  as  2.    Passed  3  times. 
Note  12.  60  words  in  3  minutes  given  41  times   below  IV-9.    Passed  10  times. 
Note  13.  Giving  rhymes  given  37  times  below  IV-io.     Passed  25  times. 

each  age  group.  That  the  subjects  of  the  "same"  age  but  in 
different  grades  are  not  exactly  the  same  is  shown  in  Table  6. 
The  subjects  of  each  age  in  the  higher  grades  average  from 
o.oi  yr.  to  0,33  yr,  different,  with  an  average  superiority  of 
0.19  yr.  This  difference,  however,  is  about  one  fourth  that 
between  the  subjects  or  different  ages  in  the  same  grades,  and 
may  be  called  the  same  for  practical  purposes.  For  convenience, 
the  groups  will  be  referred  to  as  K-5,  II-7  etc.,  the  first  member 
referring  to  the  grade,  the  second  to  the  age.  K-5  would  mean 
the  group  of  5  year  children  in  the  kindergarten,  II-7,  the  7  year 
subjects  in  Gra'de  II,  etc.  The  actual  per  cent,  that  the  subjects  in 
each  group  passed  each  test  was  calculated  and  is  shown  in  Table 
7.  Unless  otherwise  noted,  the  percentages  are  based  on  tests 
given  75%  to  100%  of  the  possible  nimiber  of  times. 

Some  of  the  groups  from  which  results  were  obtained  are  too 
small  to  have  great  reliability,  but  the  method  is  at  least  sug- 
gestive. The  results  of  14  groups  are  given.  It  is  possible  then 
to  compare  the  results  of  subjects  of  6  ages,  (6,  7,  8,  9,  10 
and  11),  that  are  in  different  grades,  and  also  to  compare  sub- 


52  CARL  C.  BRIGHAM 

jects  in  all  seven  grades  that  are  of  different  ages,  and  in  this 
way  to  determine  whether  the  dominating  factor  in  the  growth 
of  any  ability  is  that  of  grade  or  age.  The  reliability  of  the 
method  rests  only  on  its  connection  with  that  of  the  first  method 
employed. 

In  answer  to  the  question  of  whether  the  growth  of  ability  in 
the  test  of  counting  from  20  to  o  is  due  to  age  or  grade,  a  ques- 
tion which  was  unanswered  by  the  first  method,  we  may  turn  to 
the  results  shown  in  Table  7  in  which  the  subjects  of  each  age  in 
each  grade  are  shown.  The  test  of  counting  from  20  to  o  was  not 
passed  by  any  of  the  5  and  6  year  subjects  in  the  kindergarten. 
Comparing  first  the  subjects  of  different  ages  in  the  same  grade, 
the  7  year  subjects  in  Grade  i  are  16%  lower  than  the  6  year 
subjects  in  that  grade,  and  the  8  year  subjects  in  Grade  II  are 
20%  lower  than  the  7  year  subjects  in  the  same  grade,  the  older 
subjects  making  a  lower  record  in  each  case.  Comparing  the 
performance  of  the  si±>jects  of  the  same  age  but  in  different 
grades,  the  7  year  subjects  in  Grade  II  are  63%  ahead  of  the 
subjects  of  the  same  age  in  Grade  I,  while  the  8  year  subjects 
are  40%  ^  ahead  of  the  subjects  of  the  same  age  in  Grade  II. 
Allowing  for  the  retrogression  of  the  older  subjects  in  each 
group,  i.e.  assuming  that  they  should  have  done  equally  as  well 
as  the  younger  subjects  in  the  same  grade,  the  groups  in  Grades 
II  and  III  are  still  47%  and  20%  ahead  of  the  subjects  in  the 
grades  lower.  The  growth  of  ability  in  this  test  would  therefore 
appear  to  be  due  to  grade  training. 

A  rapid  growth  of  ability  in  the  test  of  counting  stamps  oc- 
curred between  Grades  I  and  III  (37%  I-II-f28%  11-111=65% 
I-III),  according  to  the  first  method,  so  that  the  same  question 
arises  as  in  the  test  of  counting  from  20  to  o.  The  test  was  not 
passed  below  group  1-6.     No  growth  with  age  is  shown  between 

iThis  test  was  given  to  but  66%  of  the  subjects  in  III-8,  the  experimenters 
assuming  that  the  other  34%  would  pass.  The  score  given,  85%,  therefore 
represents  the  ability  of  the  lowest  selection  of  III-8  subjects,  or  the  most 
conservative  estimate  of  the  ability  of  the  whole  group.  The  same  applies 
to  the  other  tests  in  III-8  given  66%  and  72%  of  the  time.  In  this  way  the 
hypothesis  that  the  tests  are  not  influenced  by  grade  training  is  given  the 
benefit  of  the  doubt. 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  53 

1-6  and  I-7,  but  a  growth  of  31%  appears  between  II-7  and  II-8. 
A  growth  with  grade  of  17%  is  shown  from  I-7  to  II-7  and  of 
25%  from  II-8  to  III-8.  This  test  shows  therefore  the  operation 
of  the  two  factors  of  age  and  grade  training. 

The  improvement  in  abihty  in  the  tests  of  counting  13  pen- 
nies, describing  pictures  and  naming  colors,  that  was  indicated 
between  the  kindergarten  and  Grade  I  by  the  first  method,  would 
refer  to  age  rather  than  grade,  for  a  greater  increase  in  each 
test  is  indicated  between  K-5  and  K-6  than  between  K-6 
and  1-6.  Above  1-6  these  abilities  are  completely  developed. 
It  could  be  maintained  that  these  tests  are  so  completely 
within  the  ability  of  the  groups  that  the  effect  of  train- 
ing would  not  be  indicated.  The  test  that  is  best  adapted 
to  show  the  influence  of  any  factor  on  a  group  is  one  that 
is  well  within  the  ability  of  the  group — the  influence  of  the  factor 
will  be  obscured  if  the  measure  is  either  too  easy  or  too  difficult. 
The  test  of  copying  the  diamond  is  a  case  in  point  and  one  well 
worth  study,  for  it  has  been  attributed  to  the  effect  of  training 
by  various  authors.  All  the  reproductions  of  the  diamond  had 
been  scored  according  to  the  arbitrary  system  outlined  in  the 
previous  discussion  of  the  personal  equation.  A  control  on  the 
factor  of  difficulty  was  obtained  by  raising  or  lowering  the  pass- 
ing mark  in  this  test.  The  percentage  passed  was  calculated  for 
each  group  for  each  of  the  5  possible  passing  marks.  The  re- 
lations indicated  in  Table  7,  where  the  passing  mark  is  Group  IV, 
were  not  changed  by  this  process  of  raising  or  lowering  the  pass- 
ing mark.  In  all  cases  the  influence  of  age  was  shown  between 
groups  1-6  and  I-7,  and  the  influence  of  grade  shown  between 
groups  K-6  and  1-6,  The  test  was  given  to  but  59%  of  the  K-5 
group,  the  experimenter  assuming  that  the  other  41%  would 
fail,  so  that  the  percentages  calculated  represent  the  performance 
of  the  best  selection  of  K-5  subjects,  or,  in  other  words,  the 
benefit  of  the  doubt  is  given  to  the  hypothesis  that  the  test  is 
influenced  by  grade  training.  If  the  other  members  of  K-5  had 
failed  according  to  the  experimenter's  assumption,  (and  this 
assumption  was  quite  justified  for  some  had  failed  to  draw  the 
square),  29%  of  the  group  would  have  passed  instead  of  50%. 


54  CARL  C.  BRIGHAM 

The  influence  of  age  indicated  in  this  test  is  as  great  if  not  greater 
than  that  due  to  training. 

The  test  of  repeating  digits,  scored  by  the  weighting  system 
previously  described,  exhibits  a  slow  but  uniform  progress 
throughout,  the  older  subjects  in  each  group  making  records  that 
are  about  the  same  or  slightly  lower  than  those  of  the  younger 
subjects  in  the  same  grade,  an  increase  showing  fairly  regularly 
from  grade  to  grade.  The  most  marked  increase  in  this  ability 
appears  between  K-6  and  1-6,  and  between  I-7  and  II-7,  possibly 
indicating  that  the  lack  of  familiarity  with  the  use  of  digits  in 
the  lowest  grades  interferes  with  this  test  as  a  measure  of 
auditory  memory. 

The  test  of  naming  the  days  of  the  week  shows  the  most 
marked  improvement  with  age  (40%)  from  K-5  to  K-6,  prac- 
tically no  improvement  (10%),  from  K-6  to  1-6,  no  improvement 
from  1-6  to  I-7,  a  very  marked  increase  with  grade  from  I-7  to 
II-7,  a  drop  from  II-7  to  II-8,  group  III-8  marking  the  complete 
development  of  the  ability.  The  test  would  appear  to  be  due  to 
the  combined  effect  of  age  and  grade.  The  tests  of  giving  the 
day  and  date  and  naming  the  months  are  passed  only  twice  in 
the  kindergarten  and  first  grade,  by  about  a  quarter  of  the  sub- 
jects in  II-7  and  II-8  without  age  increase,  while  the  subjects  in 
III-8  shows  a  most  marked  increase  due  to  grade.  Above  III-8 
these  tests  are  seldom  failed.  The  test  of  naming  the  pieces  of 
money  shows  a  slow  growth  from  8  to  11,  the  largest  increases 
appearing  from  III-9  to  IV-9  and  from  IV-io  to  V-io,  improve- 
ment with  grade  in  each  case.  Copying  the  designs  from  memory 
shows  a  growth  of  26%  from  8  to  11,  the  development  occurring 
in  two  age  steps,  from  IV-9  to  IV- 10  and  from  V-io  to  V-ii. 

The  growth  with  age  cannot  be  determined  in  the  tests  of  con- 
structing sentences  from  three  given  words,  because  they  were 
given  to  too  few  cases  below  the  third  grade.  The  results  do  not 
show  whether  III-8  is  exceptionally  high  or  III-9  exceptionally 
low.  Both  tests  show  decreases  in  ability  from  III-8  to  III-9  and 
from  V-IO  to  V-ii.  The  ability  in  the  easier  test  is  well  within 
the  range  of  the  third  and  higher  grades,  showing,  therefore,  no 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  55 

improvement.  The  improvement  in  the  second  test  develops 
from  33%  to  80%  in  three  steps,  correlating  with  Grades  IV,  V 
and  VI  in  each  case.  The  most  vital  question,  that  of  determin- 
ing whether  or  not  the  language  training  in  the  third  grade  helps 
to  make  the  construction  of  a  sentence  possible,  cannot  be  deter- 
mined owing  to  the  lack  of  material  in  the  second  grade.  The 
experimenters'  assumptions  in  not  trying  the  test  would  indicate 
this  fact,  but  this  is  not  experiment.  The  same  lack  of  material 
makes  conclusions  in  regard  to  the  rhyming  test  impossible.  The 
performance  of  IV-io  is  exceeded  only  by  VI-ii.  The  test  of 
naming  60  words  in  three  minutes  shows  two  decided  increases 
with  age  and  one  decided  drop  with  grade. 

The  foregoing  analysis  is  based  on  a  number  of  subjects  in 
each  group  too  small  to  have  any  great  significance.  The  general 
fact  of  the  correlation  of  the  tests  with  grade  remains,  and  con- 
clusions concerning  what  tests  correlate  too  highly  with  training 
can  be  answered  only  by  considering  both  methods  of  study,  and 
by  considering  only  the  largest  deviations.  The  two  most  strik- 
ing instances  are  found  in  the  tests  of  naming  the  months  and 
giving  the  date.  These  tests  undoubtedly  relate  almost  entirely 
to  training.  Less  striking  but  equally  definite  is  the  relation  of 
the  test  of  counting  from  20  to  o  to  training.  The  tests  of 
naming  the  days  of  the  week  and  counting  stamps  show  the  in- 
fluence of  age  to  an  extent  almost  as  marked  as  that  of  grade,  so 
that  while  the  development  in  these  tests  is  rapid,  the  grade  factor 
probably  exerts  only  part  of  the  influence.  Conclusions  concern- 
ing the  other  tests  are  largely  a  matter  of  opinion,  and  the  opinion 
of  the  writer  has  been  indicated  in  the  detailed  discussion. 

A  study  of  the  tests  in  relation  to  grade  by  the  first  method 
employed  may  be  made  from  Schmitt's  results.  The  author 
gives,  in  Table  I,  II,  III,  IV,  V,  VI  and  VII  on  pages  70,  71,  73, 
74,  75,  76  and  77  of  her  monograph,  the  results  of  each  subject 
in  each  grade  on  each  test.  From  these  tables  the  present  writer 
has  calculated  the  percentage  passed  in  each  test.  A  study  of 
this  sort  rests  for  its  reliability  on  the  accuracy  of  the  published 
tables,  and  the  facts  indicated  by  the  tables  do  not  always  coincide 


56  CARL  C.  BRIGHAM 

with  Schmitt's  discussion.^  The  writer  has  followed  the  tables 
rather  than  the  discussion  in  calculating  the  results.  In  the  VIII-2 
test  where  an  alternative  rank  is  given  for  counting  from  lo  to  o 
instead  of  20  to  o,  the  writer  has  considered  success  in  counting 
from  10  to  o  as  a  failure  in  counting  from  20  to  o.  In  the  line 
suggestion  test  Schmitt  recognizes  two  types  of  failure,  the 
typical  failure  according  to  Binet  of  accepting  the  suggestion  of 
the  first  three  lines,  and  the  failure  due  to  the  fact  that  the  subject 
actually  judges  the  lines  unequal  after  studying  them.  The  sec- 
ond type  of  response  Schmitt  marks  as  passed,  using  a  special 
symbol.  The  writer  has  calculated  these  percentages  separately, 
entering  the  first  or  Binet  type  of  response  under  "Line  sugges- 
tion A"  in  the  table,  and  the  second  type  under  "B."  The  V  year 
and  Adult  tests  were  omitted.  All  of  the  other  tests  were  in- 
cluded that  had  been  given  over  70%  of  the  possible  number  of 
times.  Unless  otherwise  noted,  each  test  was  given  100%  of 
the  possible  number  of  times.  Table  8  shows  the  per  cent,  that 
Schmitt's  subjects  in  each  grade  passed  each  test  in  Binet's  191 1 
scale  (Town's  translation  with  modifications).  The  table  is 
given  with  the  reservation  that  the  tables  from  which  the  per- 
centages were  calculated  might  contain  misprints,  and  that  the 
writer's  interpretation  of  the  tables  might  be  at  fault. 

Inasmuch  as  there  are  many  differences  in  procedure  in  giving 
the  tests,  and  in  the  character  of  the  schools  tested,  the  results  of 
the  two  investigations  are  not  comparable  in  respect  to  the  per- 
centage passed  in  one  grade  in  one  study  with  those  in  the  same 
grade  in  the  other  study.     The  method  used  in  determining  the 

2  In  the  discussion  (page  69)  Schmitt  gives  15  subjects  in  the  kindergarten 
failing  test  VII-4.  Table  I  shows  13.  On  the  same  page  she  gives  24  sub- 
jects failing  VIII-4.  Table  I  shows  22  failing.  In  discussing  the  results 
of  Grade  I  (page  72)  Schmitt  states  that  there  is  "more  than  50%  of  failure 
with  the  discrimination  of  weight",  while  Table  II  shows  35%  failure.  Again, 
the  tests  referred  to  specific  school  instruction  by  Schmitt  are  VII-4,  VIII-4, 
and  IX  I,  2,  3  and  4.  On  page  72,  in  discussing  the  results  of  Grade  I,  she 
says  "the  tests  below  ten  years  which  depend  upon  specific  instruction  are 
usually  not  passed  except  the  VII-4  test.  The  percentages  passed  are  as 
follows:  VII-4  =  85%;  VIII-4  =  45%;  IX-i  =  35%;  IX-2  =  75%; 
IX-3=9o% ;  IX-4=i3o%.  "Usually  not  passed"  includes,  therefore,  tests 
passed  75%  and  90%  of  the  time. 


VARIABLE  FACTORS  IN  THE  BINET  TESTS 


57 


TABLE  8 


Number  of  subjects 
VI-i,  Distinguishing  morning,  afternoon 

2,  Defining  in  terms  of  use 

3,  Copying  diamond 

4,  Counting  13  pennies 

5,  Choosing  prettier  of  faces 
VII-i,  Showing  right  hand 

2,  Describing  pictures 

3,  Executing  3  commissions 

4,  Counting  stamps 

5,  Naming  colors 
VIII-i,  Comparing  remembered  objects 

2,  Counting  backwards  from  20  to  0 

3,  Indicating  omissions   in  pictures 

4,  Giving  day  and  date 

5,  Repeating  5  digits 
IX-i,  Making  change 

2,  Defining  in  terms  superior  to  use 

3,  Naming  pieces  of  money 

4,  Naming  the  months 

5,  Comprehending  easy  questions 
X-i,  Arranging  5  weights 

2,  Copying  designs 

3,  Detecting  absurdities 

4,  Comprehending  difficult  questions 

5,  Constructing  sentence.    Two  ideas 
XII-i,  Resisting  suggestion,  A.    (Binet  scoring) 

B.  Judgment  error  counted  plus 

2,  Constructing  sentence.     One  idea 

3,  Giving  60  words  in  three  minutes 

4,  Defining  abstract  terms 

5,  Reconstructing  dissected  sentences 
XV- 1,  Repeating  7  digits 

2,  Rhyming  words  with  "obey" 

3,  Repeating  a  sentence  of  26  syllables 

4,  Interpreting  pictures 

5,  Solving  problems  from  various  facts 

Note. — All  tests  except  those  marked  (*)  were  given  all  the  possible  number  of 
times.  The  VI  year  tests  were  given  90%  of  the  time  in  Grade  I,  the  IX  year  tests 
72%  of  the  time  in  the  kindergarten,  the  XII  year  tests  70%  of  the  time  in  Grade  I, 
and  the  XII  and  XV  year  tests  95%  of  the  time  in  Grade  V. 


rade 

Passed 

Eacl 

1  Test. 

150 

Subjects. 

Grades 

K 

I 

II 

III 

IV 

V 

VI 

25 

20 

17 

21 

22 

22 

23 

96 

100* 

92 

94* 

76 

94* 

92 

100* 

92 

100* 

92 

80 

100 

72 

65 

81 

92 

95 

100 

48 

85 

100 

96 

100 

100 

92 

100 

100 

100 

100 

40 

85 

94 

95 

100 

100 

95 

94 

100 

100 

12 

45 

94 

100 

100 

64 

85 

94 

100 

100 

6* 

35 

71 

95 

86 

100 

39* 

75 

65 

100 

95 

100 

28* 

90 

94 

100 

100 

100 

6* 

30 

71 

95 

95 

95 

61* 

100 

100 

95 

100 

100 

65 

41 

57 

50 

64 

10 

35 

57 

45 

32 

60 

88 

100 

100 

100 

85 

100 

100 

100 

100 

65 

76 

100 

100 

100 

ng) 

64* 

76 

52 
100 

41 
86 

14* 
100* 

100 

57* 

71 

95 

95 

100* 

100 

43* 

82 

62 

100 

95* 

96 

7* 

29 

52 

7i 

95* 

100 

0* 

6 

10 

23 

81* 
62* 
86* 
10* 

14* 
62* 

78 
78 
70 
17 
70 
70 

58  CARL  C.  BRIGHAM 

correlation  of  the  tests  with  grade  is  the  same  as  that  used  in 
the  first  method  of  treating  the  Princeton  data,  that  of  comparing 
the  differences  between  grades  by  one-grade  and  two-grade  steps, 
of  selecting  an  arbitrary  standard  for  detect|ing  exceptional 
growth,  and  of  comparing  the  resulting  lists.  The  differences 
between  the  performance  of  each  grade  and  the  next  succeeding 
grade  were  calculated.  These  differences,  lOO  in  number,  ranged 
from  — 24%  to  +62%,  the  median  being  -f  5%  (Q=io.75%). 
The  run  of  differences  differs  from  that  found  in  the  Princeton 
study  in  two  respects,  in  having  a  lower  median  and  variability, 
and  in  containing  more  minus  deviations.  The  lower  median  and 
variability  is  due  to  the  fact  that  the  tests  were  given  over  a 
wider  range,  the  Princeton  tests  being  given  only  on  the  "up 
slope"  of  the  growth  curve,  or  not  being  given  when  the  tests 
were  any  distance  above  or  below  the  probable  range  of  ability  of 
the  group.  The  Princeton  results  showed  only  4  minus  deviations 
of  4,  3,  2,  and  1%  respectively,  while  Schmitt's  results  show  15 
such  deviations,  6  of  them  being  10%  or  over.  These  deviations 
are  probably  due  to  the  smaller  number  of  subjects,  and  if  due 
to  chance,  should  be  counteracted  by  the  precautionary  measure 
of  combining  the  indices  of  correlation  into  two-grade  steps.  71 
two-grade  differences  were  obtained  ranging  from  —  25%  to 
+  82%,  the  median  being  +10%  (Q=:zi6.5%).  4  meas- 
ures were  still  in  the  minus  direction,  one  of  these,' — 25% 
(Design  III  to  V)  is  probably  significant,  the  other  values 
of  — 6%,  — 5%  and  — 4%  having  no  significance.  Inasmuch 
as  the  variability  of  the  series  is  lower,  those  differences 
were  considered  to  be  worthy  of  special  study  that  had  the 
value  of  2Q+M,  or  were  in  excess  of  the  interquartile  range 
plus  the  median.  The  lists  of  tests  that  appear  as  showing 
marked  growth  with  grade  according  to  the  two  methods  are 
as  follows: 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  59 

One  grade  diflferences  Two  grade  differences 

higher  than  2Q4-M  higher  than  2Q4-M 

+62%,  IX-3,  Money,  K  to  I  +82%,  VIII-4,  Date,  K  to  II 

+58%,  XII-5,  Dissected,  IV  to  V  +7i%,  XII-s,  Dissected,  III  to  V 

+49%,  VIII-4,  Date,  I  to  II  +66%,  IX-3,  Money,  K  to  II 

+45%,  VIII-2,  20  to  o,  K  to  I  +65%,  IX-4,  Months,  K  to  II 

+41%,  IX-4,  Months,  I  to  II  -\-^5%,  IX-4,  Months,  I  to  III 

-f65%,  IX-i,  Change,  K  to  II 


+60%,  IX-i,  Change,  I  to  III 


+39%,  IX-5,  Comprehension,  K  to  I 
4-39%,  XII-3,  60  words,  I  to  II 

+38%,  XII-3,  60  words.  III  to  IV  +55%,  XII-5,  Dissected,  IV  to  VI 

+37%,  VII-4,  Stamps,  K  to  I  +55%,  VIII-4,  Date,  I  to  III 

+36%,  IX-2,  Definitions,  K  to  I  +54%,  VIII-2,  20  to  o,  K  to  II 

+36%,  IX-I,  Change,  I  to  II  +52%,  VII-4,  Stamps,  K  to  II 
+35%,  IX-2,  Definitions,  II  to  III  ,    „o,    v       -^     •        x  .     ttt 

+33%,  VIII-4,  Date,  K  to  I  +^7%,  X-2   Design,  I  to  III 

+45%,  XII-4,  Abstract  Def.,  I  to  III 

+29%,,  IX-I,  Change,  K-I  +44%,  XII-4,  Abstract  Def.,  II  to  IV 

+28%,  X-3,  Absurdities,  I  to  11  +43%,  XII-4,  Abstract  Def.,  Ill  to  V 

A  Study  of  the  above  lists  shows,  as  in  the  similar  study  of 
the  Princeton  data,  that  although  the  method  of  selecting  the 
exceptional  tests  is  an  arbitrary  one,  the  method  is  justified  in 
practice,  for  only  a  few  tests  (13)  appear  in  the  lists  as  signifi- 
cant. In  all,  there  were  34  tests^  studied,  and  30  differences  were 
considered  large  enough  to  be  significant.  These  30  differences 
were  confined  to  13  tests.  The  tests  of  naming  60  words  and 
defining  in  terms  of  use  drop  out  of  the  first  list  owing  to  the 
elimination  of  the  errors  of  negative  correlation.  The  design  test 
is  both  positive  and  negative,  the  ability  increasing  from  Grades 
I  to  III  and  decreasing  after  III.  The  test  of  defining  abstract 
terms  appears  according  to  the  second  nlethod  because  the 
ability  increases  with  grade  from  7%   in  I  to  95%   in  V  by 

3  No  differences  were  calculated  from  the  line  suggestion  test  owing  to 
the  possibility  of  misinterpreting  the  symbols.  Schmitt  notes  the  difference 
in  the  character  of  the  responses  from  the  suggestion  error  to  the  judgment 
error  in  passing  from  Grade  II  to  III.  The  scoring  of  the  suggestion  error 
in  the  tables  shows  an  inverse  correlation  with  Grades  II,  III,  IV  and  V, 
and  a  sudden  change  again  from  14%  in  Grade  V  to  100%  in  Grade  VI,  so 
that  there  is  probably  a  mistake.  The  scoring  of  the  responses  to  this  test 
according  to  the  strict  Binet  ruling  would  make  the  "mental  ages"  lower, 
for  many  cases  would  then  have  basal  X. 


6o  CARL  C.  B  RICH  AM 

increases  of  approximately  25%  in  each  grade.  No  conclusions 
may  be  drawn  concerning  the  easy  comprehension  test  and  the 
absurdities  test.  The  20  remaining  differences  are  confined  to  7 
tests,  those  of  naming  the  day  and  date,  naming  the  months, 
counting  from  20  to  o,  counting  stamps,  naming  money,  recon- 
structing dissected  sentences,  and  making  change.  The  first  four 
were  included  in  the  five  found  to  show  the  most  marked  influ- 
ence of  grade  in  the  Princeton  study.  The  test  of  naming  the 
pieces  of  money  did  not  show  a  marked  relation  to  grade  in  the 
latter  study,  but  this  difference  might  be  one  of  school  curriculum. 
The  test  of  naming  the  days  of  the  week  is  not  included  in  Binet's 
191 1  scale. 

In  the  Princeton  study  alternatives  were  used  in  the  making 
change  question  so  that  no  data  from  this  test  were  included  in 
the  quantitative  study.  These  data  show  the  ability  in  this  test 
developing  in  the  second  and  third  grades,  the  test  being  passed 
only  twice  in  the  kindergarten  and  first  grades,  and  generally 
passed  above  the  third.  The  data  in  the  test  of  reconstructing 
dissected  sentences  show  very  few  passing  the  test  below  grade 
V  with  approximately  three  fourths  passing  in  V  and  VI.  In  so 
far  as  the  Trenton  experimenting  was  applied  to  a  few  subjects 
in  the  regular  grades  below  the  seventh,  this  test  was  rarely 
passed  in  the  third  and  fourth  grade,  passed  about  5%  in  V,  and 
almost  universally  passed  in  VI,  VII  and  VIII.  The  number  of 
subjects  in  each  grade  is  small  in  the  Trenton  experiment,  but 
each  test  was  separately  scored,  i.e.  each  part  of  the  dissected 
sentence  test,  each  part  of  the  absurdity  test  etc.  Each  of  the 
three  parts  of  the  dissected  sentence  test  showed  the  same  growth 
between  the  same  grades,  and  this  growth  was  more  marked 
than  that  in  any  other  test.  The  evidence  concerning  these  two 
tests,  therefore,  supports  the  evidence  from  Schmitt's  results. 

The  quantitative  analysis  of  the  Princeton  data  and  Schmitt's 
data  would  indicate  that  the  tests  of  counting  stamps,  counting 
from  20  to  o,  naming  the  days  of  the  week,  giving  the  day  and 
date,  naming  the  months,  naming  the  pieces  of  money,  making 
change  and  reconstructing  dissected  sentences  were  influenced  to 
a  considerable  extent  by  grade  training.     The  performance  in 


VARIABLE  FACTORS  IX  THE  BINET  TESTS  6i 

certain  of  these  tests  (days,  date  and  months)  may  be  the  result 

of  specific  school  training  in  the  tests  themselves,  while  others 

(perhaps  the  tests  of  counting  stamps,  counting  from  20  to  o, 

and  reconstructino-  dissected  sentences)  mav  involve  a  transfer 

.      .  .     *■ 

effect  in  the  application  of  the  content  of  the  grade  in  a  new  way. 

The  fact  that  the  tests  correlate  very  highly  with  grade  training 
does  not  show  that  the  tests  are  worthless,  but  it  does  show  that 
they  should,  perhaps,  be  placed  in  another  scale,  or  should  at 
least  be  placed  on  a  different  footing  than  those  that  test  capacity 
irrespective  of  attainments. 

One  of  the  best  tests*  of  intelligence  is  the  determination  of 
what  an  individual  can  do  with  the  training  he  has  received,  but 
tests  of  this  sort  rest  on  the  assumption  that  the  individual's 
opportunities  have  been  determined.  The  importance  of  tests  of 
information  in  cases  of  alienation  presenting  a  picture  of  deteri- 
oration is  recognized.  The  important  change  to  be  made  is  not 
the  elimination  of  such  tests  from  intelligence  scales,  but  their 
standardization  on  a  different  basis.  The  diagnostic  value  of 
such  tests  rests  not  in  the  mechanical  memorizing  of  a  time 
series  such  as  that  of  the  months,  but  in  the  ability  to  apply 
such  a  series.  In  pointing  out  this  fact  Katzenellenbogen  (37) 
suggests  that  the  months  test  be  given  in  some  such  manner  as 
"If  somebody  asks  you  in  November  to  return  three  months  later, 
what  month  would  it  be?"  Decroly  and  Degand  also  suggest 
that  the  mechanical  tests  of  counting  and  naming  the  days  of  the 
week  and  months  be  modified  in  some  such  manner. 

*  The  writer  recalls  two  cases  in  which  the  failure  in  tests  which  involved 
the  application  of  training  was  very  significant.  The  first  was  that  of  a 
woman  of  about  30,  a  parole  patient  in  a  hospital  for  the  insane,  who  had 
never  shown  any  marked  symptoms  other  than  a  history  of  intellectual  in- 
feriority. This  patient  passed  practically  all  of  the  Binet  tests  in  the  IX, 
X  and  XII  year  groups,  but  failed  completely  in  the  test  of  making  change. 
This  observation  was  later  checked  up.  Another  case  of  a  woman  of  22, 
in  the  same  hospital,  presented  a  border-line  psychoneurotic  picture  perhaps, 
but  no  marked  symptoms  other  than  a  history  of  intellectual  inferiority.  She 
passed  in  a  great  many  of  the  difficult  tests  in  the  upper  years  but  had  great 
difficulty  in  telling  time.  Both  cases  had  lived  under  very  good  home  con- 
ditions and  had  mingled  with  people  of  ability.  A  great  many  tests  of  capa- 
city were  given,  but  the  most  illuminating  evidence  of  their  mental  status 
came  from  the  two  tests  mentioned. 


62  CARL  C.  BRIGHAM 

Comparing  the  conclusions  of  this  study  with  other  investiga- 
tions, the  agreement  is  fairly  close.  Schmitt's  results  do  not 
support  her  suggestion  that  the  definitions  test  relates  to  specific 
school  instruction.  The  other  tests  which  she  refers  to  this 
factor  (stamps,  date,  20  to  o,  change,  months  and  money)  show 
the  influence  to  a  marked  extent.  Binet  in  classifying  some  of 
the  tests  referred  the  tests  of  copying  a  sentence,  reading  for 
memories,  writing  from  dictation,  copying  a  diamond,  counting 
backwards  and  making  change  to  scholastic  training.  The  first 
three  tests  were  not  included  in  this  investigation.  The  diamond 
test  showed  the  influence  of  age  to  be  as  great  if  not  greater  than 
that  of  school  training.  The  last  two  tests  showed  a  marked 
influence  of  training,  Binet  referred  the  tests  of  counting  13 
pennies,  naming  four  colors,  naming  the  days  of  the  week  and 
enumerating  the  months  to  home  training.  The  last  two  showed 
a  marked  influence  of  school  training.  The  results  of  the  present 
investigation  agree  with  those  of  Chotzen  in  finding  no  effect  or 
very  little  effect  of  training  in  the  tests  of  copying  the  diamond, 
repeating  digits,  describing  pictures,  counting  13  pennies,  naming 
colors,  comparing  remembered  objects,  defining  in  terms  of  use 
and  superior  to  use,  and  in  finding  marked  influence  of  this 
factor  in  the  test  of  naming  the  days  of  the  week. 

The  methods  used  in  analysing  the  results,  especially  the  sec- 
ond method,  reveal  several  suggestive  relations  between  the 
tests  and  the  school  grades.  There  is  a  general  correlation  be- 
tween the  tests  and  the  grades,  a  correlation  that  is  very  necessary 
to  establish,  for  there  is  also  a  general  correlation  between  intelli- 
gence and  grade.  In  analysing  the  results  of  the  individual  tests 
by  comparing  the  results  of  subjects  of  the  same  age  in  different 
grades,  and  of  subjects  of  different  ages  in  the  same  grade 
(Table  7),  it  was  seen  that,  as  a  general  rule,  the  growth  in  any 
particular  ability  occurred  in  passing  from  grade  to  grade,  not  in 
passing  from  age  to  age  within  one  grade.  In  fact  in  only  half 
of  the  cases  in  which  the  subjects  of  two  ages  in  one  grade  may 
be  compared  do  the  older  subjects  make  records  that  are  higher 
than  those  of  the  younger  ones,  and  only  10%  of  these  gains  are 
over  20%.     If  the  groups  were  considered  to  be  equal  in  all 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  63 

cases  in  which  their  records  were  within  10%  of  each  other, 
equahty  occurs  in  exactly  50%  of  the  cases.  Of  the  remainder, 
20%  of  the  groups  were  lower,  while  in  only  30%  of  the  cases 
are  the  older  subjects  actually  higher  than  the  younger  subjects 
of  the  same  grade.  Some  of  the  cases  of  retrogression  could 
well  be  accidental,  but  they  occur  too  frequently  to  be  due 
entirely  to  chance. 

Applying  the  same  general  method  to  the  cases  in  which  groups 
of  the  same  age  but  in  different  grades  were  compared,  5%  of 
the  groups  in  a  higher  grade  showed  lower  scores,  the  results 
correspond  in  43%  of  the  cases,  while  52%  showed  definite 
improvement.  This  might  indicate  that  there  is  a  higher  correla- 
tion between  the  tests  and  grade  than  between  the  tests  and  age. 
The  fact  that  the  comparison  of  children,  of  different  ages  in  the 
same  grade  showed  the  older  children  making  lower  records  in 
20%  of  the  cases,  equal  records  in  50%  of  the  cases  and  higher 
records  in  only  30%,  would  confirm  the  general  diagnostic  value 
of  the  tests  if  Bonser's  interpretation  of  this  phenomena  is  cor- 
rect. Bonser  (12)  applied  various  sorts  of  reasoning  tests  to 
children  in  the  fourth,  fifth  and  sixth  school  grades.  In 
summarizing  the  results  of  the  tests  in  the  dift'erent  grades,  he 
says,  'Tn  the  contrast  with  grade  progress  and  progress  with  age, 
in  the  generally  superior  showing  made  by  the  younger  groups 
of  children  of  any  grade  when  contrasted  with  the  older  pupils 
of  the  grade,  and  in  the  fairly  substantial  percentage  of  pupils 
from  lower  grades  found  in  the  highest  quartile  of  ability  for  all, 
it  is  shown  that  native  capacity  is  measured  to  a  high  degree  by 
the  tests." 

In  conclusion,  the  results  shown  in  this  chapter  would  indi- 
cate a  correlation  between  the  individual  tests  studied  and  the 
school  grades,  this  correlation  being  high  enough  in  some  cases 
to  show  the  actual  eft'ect  of  training.  In  answer  to  the  general 
objection  that  since  one  demonstration  of  the  accuracy  of  the 
tests  rests  on  their  correlation  with  school  grades,  the  school 
grades  are  the  real  measure  of  intelligence  and  the  mental  tests 
superfluous,  it  is  only  necessar}'  to  point  out  that  intelligence  tests, 
besides  affording  the  opportunity  for  accurate  standardization. 


64  CARL  C.  BRIGHAM 

also  detect  the  subject's  potential  abilities  independent  of  his  past 
performance.  The  school  measure  indicates  mental  defect  in 
cases  of  gross  retardation,  but  it  does  not  indicate  exceptional 
ability. 

Schmitt's  contention  that  the  school  represents  a  standard 
environmental  situation,  and  a  measure  of  a  subject's  ability 
should  include  a  measure  of  the  adequacy  of  his  reaction  to  this 
situation,  is  well  founded.  It  is  not,  however,  a  criticism  of  the 
Binet  scale,  for  the  scale  aims  to  test  native  capacity.  At  the 
Buffalo  conference  (15)  on  the  Binet  scale,  the  following  ques- 
tion was  raised, — "What  is  it,  after  all,  that  the  scale  aims  to 
test?"  The  question  was  answered  by  "We  believe  that  current 
misconceptions  as  to  the  aim  of  the  scale  should  be  removed.  It 
is  not  intended  to  test  the  emotional  or  volitional  nature,  but 
primarily  intelligence  (judgment)."  To  this  list  might  be  added 
the  assertion  that  the  scale  was  not  intended  to  test  a  child's 
reaction  to  the  school  situation,  or  to  furnish  an  outline  for 
taking  a  record  of  his  life  history. 

Rogers  and  Mclntyre  (54)  would  also  have  mental  tests  in- 
clude tests  dependent  on  both  school  and  home  training.  This 
general  trend  of  present  day  discussion  is  a  reversion  to  Binet's 
1908  type  of  scale,  a  tendency  to  which  Binet  was  in  opposition. 
The  probable  solution  rests  in  eliminating  from  the  scale  the  tests 
involving  training,  and  in  constructing  a  standardized  scale  of 
another  sort  for  the  estimation  of  the  individual's  reaction  to  the 
school  situation  in  terms  of  the  length  of  time  that  he  has  met 
that  situation.  That  such  a  scale  is  not  a  matter  of  speculation 
is  shown  by  the  number  of  scales  now  on  the  market  for  measur- 
ing handwriting,  spelling,  composition,  arithmetical  ability,  etc. 
Tests  of  native  capacity  and  tests  dependent  on  school  and  en- 
vironmental training  cannot  be  standardized  on  the  same  basis,  for 
they  are  essentially  different  measures.  Measures  of  the  first  sort 
may  perhaps  be  correlated  with  age,  while  measures  of  the  other 
sort  can  be  correlated  only  with  opportunity. 


V.  SEX  DIFFERENCES 

The  investigators  who  have  studied  the  influence  of  sex  differ- 
ences on  the  Binet-Simon  tests  have  used  two  methods,  that  of 
comparing  the  "mental  ages"  or  total  scores  of  subjects  of  each 
sex,  and  that  of  comparing  the  per  cent,  that  the  subjects  of  each 
sex  pass  each  test.  The  first  method  throws  no  light  on  the 
individual  tests,  inasmuch  as  one  sex  may  be  superior  in  one 
test  and  inferior  in  another  so  that  the  total  score  will  balance 
the  influence  of  this  factor.  Inasmuch  as  the  scale  is  founded  on 
the  principle  that  sex  differences  do  not  exist,  it  is  important  to 
study  the  individual  tests,  and  to  determine  the  accuracy  of  this 
assumption. 

The  Princeton  data  are  available  for  a  study  of  this  sort.  352 
subjects  (187  boys  and  165  girls)  between  the  ages  6  and  12 
were  examined.  The  method  of  study  adopted  was  that  of  com- 
paring the  results  of  non-selected  boys  and  girls  of  each  age,  and, 
as  a  check  on  this  method,  of  comparing  the  results  of  selected 
boys  and  girls  of  four  ages. 

Inasmuch  as  the  subjects  of  each  chronological  age  are  dis- 
tributed over  a  range  of  one  year  (the  6  year  subjects  for  exam- 
ple being  distributed  from  6.0  to  6.9),  the  actual  average  age  of 
the  subjects  of  each  age  was  computed  to  make  sure  that  no 
differences  might  appear  due  to  the  chance  selection  of  subjects 
at  either  extreme.    These  averages  are  shown  in  Table  9. 

TABLE  9 
Actual  Average  Chronological  Age  of  Boys  and  Girls  in  Each  Age  Group. 


BOYS 

GIRLS 

Number 

of 

Average  Age 

Number  of 

Average  Age 

Subjects 

(M.V.) 

Subjects 

(M.V.) 

Age 

6 

Zl 

6.58   (0.20) 

2Z 

6.51    (0.20) 

Age 

7 

29 

7.50   (0.29) 

31 

7.39   (0.26) 

Age 

8 

24 

8.48   (0.29) 

28 

8.48   (0.22) 

Age 

9 

20 

9.46  (0.27) 

22 

9.54  (0.26) 

Age 

10 

31 

10.46   (0.25) 

23 

10.37   (0.30) 

Age 

II 

28 

11.59   (0.22) 

20 

11.52   (0.27) 

Age 

12 

18 

12.43   (0.30) 

18 

12.57   (0.24) 

66 


CARL  C.  BRIGHAM 


A  perusal  of  this  table  shows  that  the  subjects  agree  closely 
both  in  their  average  and  in  their  variability.  The  12  year  boys 
are  actually  0.14  yr.  younger  than  the  girls  of  the  same  age 
group.  The  7  year  boys  are  o.  1 1  yr.  older  than  the  7  year  girls. 
All  other  differences  are  less  than  o.io  yr.  The  correspondence 
is  close  enough  for  all  practical  purposes,  but  these  differences 
must  be  taken  into  consideration  before  drawing  final  conclusions. 

The  352  non-selected  subjects  from  6  to  12  were  distributed 
throughout  the  kindergarten,  special  class,  and  first  six  minus  and 
plus  grades  as  shown  in  Table  10. 

TABLE  10 
Age  in  Grade  Distribution  of  187  Boys  and  165  Girls,  6  to  12  Years  of  Age. 


Age 

6 

7 

8 

9 

10 

II 

12 

Totals 

Sex 

B 

G 

B   G 

B   G 

B 

G 

B 

G 

B 

G 

B 

G 

Special  Class 

2 

I 

3 

3 

3 

I 

13 

Kindergarten 

8 

3 

II 

Grade  I- 

13 

4 

8    9 

I     I 

I 

37 

Grade  I 

14 

14 

9    9 

3     I 

I 

SI 

Grade  II- 

2    2 

2    4 

2 

12 

Grade  II 

2 

7  10 

6    9 

2 

3 

I 

40 

Grade  Ill- 

3 

4 

2 

I 

I 

I 

12 

Grade  III 

2 

8  10 

5 

8 

5 

5 

I 

r 

45 

Grade  IV- 

I 

5 

I 

2 

2 

3 

I 

IS 

Grade  IV 

I 

I 

5 

6 

10 

4 

I 

2 

3 

2 

35 

Grade  V- 

I 

I 

I 

3 

3 

9 

Grade  V 

7 

II 

10 

6 

2 

6 

42 

Grade  VI- 

I 

I 

2 

Grade  VI 

I 

10 

6 

6 

5 

28 

Totals 

37  23 

29  31 

24  28 

20 

22 

31 

23 

28 

20 

18 

18 

352 

It  is  generally  conceded  that  a  difference  exists  in  the  reactions 
of  the  sexes  to  the  school  curriulum,  the  girls  in  the  long  run  mak- 
ing better  progress  in  school  work  than  the  boys.  A  study  of 
Table  10  shows  that  in  general  the  girls  have  a  slightly  higher 
distribution  than  the  boys,  these  relations  being  more  clearly 
indicated  in  Table  11  in  which  the  average  grade  of  the  subjects 
of  each  age  and  sex  is  shown.  In  computing  the  average  grade. 
the  kindergarten  was  counted  o;  Grade  I — ,  0.5;  Grade  I+,  i.o; 
Grade  II — ,  1,5;  etc.  Each  subject  in  the  special  class  was  as- 
signed a  grade  0.5  lower  than  the  lowest  subject  of  his  age  (o  be- 
ing the  smallest  value  given),  on  the  theory  that  each  subject  in 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  67 

the  special  class  was  less  satisfactory  than  any  of  his  comrades  in 
the  regular  class.  The  fact  that  there  were  no  girls  in  the  special 
class  would  cause  an  unduly  exaggerated  difference  between  the 
average  grades  of  the  boys  and  girls.  For  this  reason,  the 
average  grades  of  the  boys,  including  and  excluding  the  special 
class  cases,  were  separately  figured,  these  values  being  separately 
shown  in  Table  11  under  Boys  A  (the  average  grade  including 
the  special  class  cases),  and  Boys  B  (the  average  grade  exclud- 
ing the  classes).  Had  the  special  class  subjects  been  in  the  regu- 
lar grades,  they  would  have  lowered  the  average  of  each  group, 
so  that  the  two  values  may  be  taken  only  as  limits,  the  values 
under  "Boys  A"  being  the  lower  limit,  and  those  under  "Boys  B," 
the  upper  limit. 

TABLE  II 
Actual  Average  Grade  of  Boys  and  Girls  in  Each  Age  Group. 


BOYS  A 

BOYS  B 

GIRLS 

No. 

Average  Age 
(M.V.) 

No. 

Average  Age 
(M.V.) 

No. 

Average  Age 
(M.V.) 

Age 

6 

Z7 

0.55  (0.34) 

35 

0.59  (0.33) 

23 

0.87  (0.35) 

Age 

7 

29 

1.24  (0.64) 

28 

1.29  (0.63) 

31 

1.31  (0.65) 

Age 

8 

24 

1.94(0.91) 

21 

2.21  (0.65) 

28 

2.25  (0.59) 

Age 

9 

20 

2.48(1.04) 

17 

2.91  (0.69) 

22 

2.98  (0.62) 

Age 

10 

31 

3.92  (0.71) 

31 

3.92(0.71) 

23 

4.19  (0.80) 

Age 

II 

28 

4.66  (1.20) 

25 

5.04  (0.77) 

20 

4.83  (0.88) 

Age 

12 

18 

4.72(0.91) 

17 

4.82  (0.88) 

18 

503  (0.59) 

Table  1 1  shows  that  the  scholastic  ability  of  the  girls  as  indi- 
cated by  the  average  grade  is  uniformly  higher  than  that  indicated 
by  the  lower  limit  of  the  boys,  and  is  below  the  upper  limit  of  the 
boys  in  only  one  case  (at  11  years).  A  slight  sex  difference  in 
school  work  in  favor  of  the  girls  may  therefore  be  assumed  at  the 
outset.  It  is  significant  that  the  upper  limit  of  the  11  year  boys 
is  higher  than  that  of  the  12  year  boys,  and  that  the  lower  limits 
show  a  difiference  of  but  0.06.  This  would  indicate  a  poor  selec- 
tion of  12  year  boys,  or  a  superior  selection  of  11  year  boys. 
Both  measures  of  the  scholastic  ability  of  the  boys  show  a  gener- 
ally higher  variability  than  that  of  the  girls. 

From  Table  9  it  may  be  seen  that  the  growth  in  the  actual 
average  age  of  each  sex  is  not  uniform  from  year  to  year,  the 
minimum  increase  for  boys  being  0.84  yr.  (from  11  to  12),  and 


6S  CARL  C.  BRIGHAM 

for  girls  0.83  yr.  (from  9  to  10),  while  the  maximnm  increase 
for  boys  is  1.13  yr.  (from  10  to  11),  and  for  girls  1.15  yr.  (from 
10  to  11).  A  more  marked  lack  of  regularity  in  the  growth  of 
scholastic  ability  from  year  to  year  as  measured  by  the  average 
grade  is  shown  in  Table  11,  no  increase  being  shown  by  the  12 
year  boys  over  the  1 1  year  lx)ys,  while  the  10  year  boys  show  an 
increase  of  1.44  to  i.oi  grades  over  the  9  year  boys.  In  the  same 
way  the  10  year  girls  show  an  increase  over  the  9  year  girls  that 
is  nearly  three  times  that  of  the  7  year  girls  over  the  6  year  girls, 
while  the  increase  of  the  7  year  girls  over  the  6  year  girls  is 
twice  that  of  the  12  year  girls  over  the  11  year  girls.  These 
relations  indicate  that  the  selection  of  subjects  is  not  uniform  at 
each  age.  The  subjects  of  any  one  age  may  be  either  a  superior 
or  inferior  selection  of  all  children  of  that  age,  and  there  is  no 
reason  for  supposing  that  this  random  sample  of  superior  or 
inferior  subjects  of  any  age  will  correspond  to  a  similar  sampling 
of  the  subjects  of  the  opposite  sex  of  the  same  age. 

The  process  of  calculating  the  percentage  that  the  boys  and 
girls  of  each  age  pass  each  test  is  extremely  simple,  but  the 
conclusion,  that  the  differences  found  between  the  percentage 
passed  by  the  sexes  at  each  age  may  be  attributed  to  sex  differ- 
ences, is  not  justified  unless  all  the  variable  factors  are  known. 

A  previous  chapter  showed  variations  in  the  tests  due  to  the 
influence  of  the  personal  equation  of  the  experimenters.  To 
avoid  this  variable  influence,  only  those  tests  were  studied  that 
showed  that  they  were  free  from  the  influence  of  this  factor. 
Inasmuch  as  each  experimenter  examined  approximately  the  same 
number  of  boys  and  girls  of  each  age,  any  influence  of  this  factor 
would  be  equalized,  provided,  of  course,  that  there  were  no  differ- 
ences in  the  reaction  of  the  experimenters  to  the  two  sexes.  In 
the  detailed  study  of  the  design  test,  it  was  found  that  experi- 
menter C  was  more  lenient  in  marking  girls  than  boys.  The 
possibility  of  a  similar  interpretation  in  a  few  other  tests  was 
suggested,  but  not  demonstrated.  In  analysing  the  results  for 
sex  differences,  however,  the  possibility  of  such  an  interpretation 
must  be  kept  in  mind. 

Another  possible  source  of  error  is  that  due  to  incomplete  data. 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  6g 

The  experimenters,  in  giving  the  tests,  would  give  only  those 
within  the  approximate  range  of  the  subject,  so  that  each  test 
would  be  given  to  a  superior  selection  of  children  below  the 
normal  range  of  the  test,  and  to  an  inferior  selection  of  subjects 
above  this  range,  a  process  tending  to  make  the  apparent  growth 
of  an  ability  less  than  the  probable  real  growth.  In  comparing 
the  results  of  the  sexes,  however,  it  is  not  necessary  to  have  ac- 
curate results  on  the  growth  of  an  ability,  but  results  which  have 
the  same  determining  factors.  If  the  experimenters  gave  the 
test  to  approximately  the  same  proportions  of  boys  and  girls  at 
each  age,  a  comparison  of  the  percentage  passed  is  legitimate, 
even  if  a  small  proportion  of  the  whole  group  were  actually 
tested,  for  the  proportion  would  include  the  same  selection  of 
subjects.  The  number  of  boys  and  girls  at  each  age,  and  the 
percentage  that  each  test  was  given  to  these  subjects  are  shown 
in  Table  12.  The  test  of  counting  13  pennies,  for  example,  was 
given  Tfy  times  to  6  year  boys,  or  100%  of  the  possible  number 
of  times,  while  the  test  of  counting  from  20  to  o  was  given  2y 
times  to  the  same  group,  or  73%  of  the  possible  number  of 
times.  Column  A  shows  the  total  number  of  times  each  test  was 
given  to  all  of  the  boys  and  girls.  Column  B  gives  the  average 
age  of  all  the  boys  and  girls  to  whom  each  test  was  given.  The 
average  given  in  this  case  is  not  the  actual  average  derived  from 
the  actual  chronological  age  of  each  subject  figured  in  tenths,  but 
the  weighted^  average,  the  whole  numbers  6,  7,  8,  9,  10,  11,  and 
12  being  used. 

Table  12  shows  a  very  close  correspondence  between  the  per- 
centage that  each  test  was  given  to  boys  and  girls  of  each  age,  so 
that  the  error  due  to  incomplete  data,  though  present,  is  present 
to  the  same  extent  in  the  results  of  both  sexes,  and  may  be 
disregarded.  A  fairly  close  correspondence  in  the  average  age 
of  all  the  boys  and  girls  to  whom  each  test  was  given  is  also 
indicated  in  Table  12.    In  the  test  of  counting  stamps  there  is  an 

^  For  example,  in  the  test  of  counting  13  pennies,  the  average  age  of  the 

boys  to  whom  the  test  was  given  is, — 

(37x6)  +  (28x7)  +  (i6x8)  +  (8x9)+(7xio)  +  (3xii)  +  (ixi2)  _  _  ,^  ^^^^^^ 
_ 7.33  >ears 


TO  CARL  C.  BRIGHAM 

TABLE  12 
Percentage  that  Each  Test  Was  Given  to  Boys  and  Girls  of  Each  Age,  the 
Total  Number  of  Times  Each  Test  Was  Given  to  Each  Sex  and  the 
Average  Age  of  All  Subjects  of  Each  Sex  to  Whom  Each  Test  Was 
Given. 

A  B 

Chronological  age  6      7      8      9     10    11     12  Total   Average 

number    age  of 
Number  of  subjects  Boys    37    29    24    20    31    28     18     of        subjects. 

Number  of  subjects  Girls    23    31    28    22    23    20    18  times  (weighted) 

given 

Counting  13  pennies         Boys  100    97    67    40    23     1 1      6    100  7.33 

Girls  100    94    68    41    26    10    Ii      90  7.56 

Describing  pictures  Boys  100    90    67    45    26    11      6    100  7.38 

Girls  100    94    68    41    30    20    11      93  7.66 

Copying  diamond  Boys  100    93    63    60    32     14    17     108  7.30 

Girls  100    94    61    64    3S    20    II      97  7.74 

Naming  colors  Boys  lOO    93    67    45    23     11      6    100  7-35 

Girls  100    94    68    41    30    15    11      92  7.62 

Counting  from  20  to  0     Boys     7^,    97    83    80    61     21     44     124  8.18 

Girls     74    71    79    77    5-'    35    28    102  8.25 

Counting  stamps  Boys    65    97    88    80    61     21    44    122  8.23 

Girls    83    87    79    82    52    35    39    112  8.23 

Repeating  all  digits  Boys    95  100  100  100  100  100  100    185  8.75 

Girls     96    97    96  100  100  100  100    162  8.78 

Naming  days  of  week      Boys    92  100    83    80    61     21    44    132  8.04 

Girls    96    90    82    82    52    33    28    115  8.10 

Giving  day  and  date        Boys    43    76    88    95    84    64    89     138  8.10 

Girls    78    77    93  100    78    73    72    136  8.70 

Naming  the  months         Boys    41     79    79    95    81     54    78     130  8.90 

Girls    39    65    93  100    70    63    61    117  8.84 

Naming  money  Boys    27    62    67    90    97    64    78    124  9.21 

Girls     43    39    86    93  100    80    67    iiS  9. 11 

Copying  designs  Boys     16    31     67    85    94    79    78    113  9.56 

Girls     26    19    37    86    96    80    67      97  9.46 

3  words  in  sentence        Boys      8    31     63    90  100    93  100    120  9.79 

Girls    26    26    68    86  100    93    94    iii  9.36 

60  words  in  3  minutes     Boys     11     21     38    70    81     93    89     100  9.92 

Girls     30     10    32    30    74    90    78      79  9.75 

Giving   rhymes  Boys      8    21     25     50    74    89    94      90  10.08 

Girls     13     13    36    43     74    90    83      77  9.92 

Defining  "fork"  etc.        Boj's    38    62    50    55    48    25     17      80  8.35 

Girls     61    63    61    68    39    20     11      81  8.09 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  71 

actual  correspondence.  The  greatest  difference  is  that  of  0.6  yr. 
in  the  test  of  giving  the  date.  The  differences,  on  the  whole,  are 
small,  but  must  be  taken  into  consideration  when  comparing  the 
percentages  that  all  boys  and  girls  pass  each  test. 

Two  methods  are  available  for  studying  the  influence  of  sex 
differences  on  the  individual  tests.  The  first  is  that  of  comparing 
the  results  of  boys  and  girls  of  each  age  on  each  test.  This 
method  is  affected  by  the  chance  selection  of  superior  or  inferior 
subjects,  and  the  results  can  have  no  meaning  unless  the  relations 
of  the  groups  of  each  age  of  the  same  sex  are  understood.  For 
example,  the  fact  that  the  12  year  boys  are  36%  lower  than  the 
12  year  girls  in  the  test  of  naming  the  months  has  no  significance 
as  an  isolated  finding,  for  its  significance  is  modified  by  the 
additional  fact  that  this  group  of  12  year  boys  is  10%  lower 
than  the  9  year  boys,  12%  lower  than  the  10  year  boys,  and  g% 
lower  than  the  1 1  year  boys  on  the  same  test. 

The  other  method  is  that  of  comparing  the  per  cent,  that  all 
subjects  of  each  sex  pass  each  test.  This  method  avoids  the 
factor  of  variations  in  the  results  due  to  a  chance  superiority  of 
one  age  group  over  the  other  of  the  opposite  sex,  but,  at  the 
same  time,  it  tends  to  obscure  the  magnitude  of  the  differences 
that  might  occur.  The  most  reliable  differential  measure  be- 
tween two  groups  is  one  that  is  well  within  the  range  of  ability 
of  the  groups.  The  difference  will  be  obscured  if  the  measure  is 
too  easy  or  too  difficult.  A  comparison  of  the  results  of  all 
subjects  would,  in  this  way,  tend  to  minimize^  the  magnitude  of 
the  real  difference  between  the  groups.  Furthermore,  there  is  a 
possibility  that  one  sex  might  acquire  an  ability  first,  but  even- 
tually be  surpassed  by  the  other.  The  per  cent,  that  all  subjects 
passed  would  show  no  deviation,  because  the  two  tendencies 
would  balance. 

2  For  example,  if  there  were  20  subjects  of  each  age  and  of  each  sex  from 
6  to  12,  and  a  certain  test  were  passed  by  75%  of  the  6  year  girls,  and  by 
all  of  the  7,  8,  9,  10,  11  and  12  j^ear  girls,  by  50%  of  the  6  year  boys,  75% 
of  the  7  year  boys  and  all  of  the  remaining  groups,  the  total  percentage 
passed  for  all  girls  would  be  96%,  and  for  all  boys,  89%.  The  differential 
character  of  the  test  is  indicated  by  the  value  7%,  while  its  actual  differential 
character,  just  within  the  range  of  ability  of  the  groups,  is  25%. 


72  CARL  C.  BRIGHAM 

Neither  method,  then,  is  entirely  satisfactory,  the  first  because 
it  would  tend  to  exaggerate  chance  differences,  the  second  because 
it  would  tend  to  obscure  real  differences.  The  method  used  in 
this  study  is  that  of  comparing  the  results  of  non-selected  and 
selected  subjects  of  each  age  and  sex,  studying  first  the  general 
growth  of  each  ability  from  age  to  age  within  each  sex,  and  using 
the  per  cent,  that  all  subjects  pass  each  test  to  determine  the  cor- 
relation between  the  results  of  non-selected  and  selected  subjects. 

Table  13  shows  the  percentage  of  proportion"  that  the  boys  and 
girls  of  each  age  pass  each  test,  the  percentage  that  all  boys  and 
girls  pass  each  test,  the  actual  percentage  that  the  boys  are  su- 
perior to  (-|-)  or  inferior  to  ( — )  the  girls  of  each  age,  the  differ- 
ence between  the  average  age  of  all  boys  and  girls  to  whom  each 
test  was  given,  and  the  dift'erence  between  the  percentage  that 
all  boys  and  girls  pass  each  test. 

The  differences  between  the  performance  of  the  boys  and  girls 
at  each  age  have  no  meaning  unless  the  general  growth  of  the 
abilities  in  each  sex  is  first  understood.  Studying  first  the  re- 
sults of  the  187  non-selected  boys  shown  in  the  first  seven 
columns  of  Table  13,  it  may  be  seen  that  the  growth  of  ability 
in  each  test  is  rather  irregular.  The  test  of  naming  the  months, 
for  example,  shows  a  slight  decrease  from  9  to  12.  The  dift'er- 
ences  between  the  percentage  performances  of  the  subjects  of 
each  age  and  those  of  the  preceding  age  were  calculated.     The 

12  year  group,  compared  to  the  11  year  group,  is  -|-ii%  on  the 
test  of  giving  the  date,  — 9%  on  the  test  of  naming  the  months 
etc.  61  differences  were  thus  obtained,  varying  in  magnitude 
from  — 15%  to  +36%,  the  median  being  +8%   (Q=975%)- 

13  of  the  deviations  (21  % )  were  minus  values.  The  largest  nega- 
tive deviations  occurred  in  the  tests  of  naming  colors  ( — 15%,  7 
to  8),  naming  money  ( — 15%,  11  to  12),  and  constructing  a 
sentence  containing  two  ideas  ( — 13%,  8  to  9).  The  remaining 
10  minus  deviations  were  less  than  10%. 

3  The  proportion  given  is  the  number  of  times  a  test  was  given  over  the 
number  of  times  a  test  was  passed.  No  percentages  were  calculated  for 
tests  given  less  than  12  times,  and  no  percentages  are  given  for  the  defini- 
tions tests  on  account  of  the  small  number  of  times  they  are  given  to  all 
subjects. 


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74  CARL  C.  BRIGHAM 

An  index  of  the  growth  from  year  to  year  was  obtained  by 
calculating  the  average  percentage  increase  from  one  age  group 
to  another.  For  example,  the  7  year  boys  were  26%  higher  than 
the  6  year  boys  in  the  test  of  naming  colors,  5%  higher  in  naming 
the  date  etc.  The  average  of  the  10  possible  comparisons  between 
6  and  7  year  boys  shows  that  the  latter  averaged  16.1%  higher 
than  the  former.  The  average  increases  in  percentage  passed 
from  year  to  year  are  as  follows, — 6  to  7=16.  i  %  ;  7  to  8^13.5% 
8  to  9=8.7%;  9  to  10=11.2%;  10  to  11^6.0%;  and  11  to 
12=0.2%.  These  figures  show  strikingly  the  irregularity  of 
the  growth  from  age  to  age.  Comparing  these  average  percent- 
age increases  in  tests  with  the  averages  shown  in  Tables  9  and  11, 
there  is  no  observable  relation  between  this  increase  and  the  in- 
crease in  average  age  from  age  to  age,  or  the  increase  in  average 
grade  from  age  to  age.  The  smallest  increase  in  the  tests 
(0.2%,  II  to  12)  coincides  with  the  smallest  increase  in  average 
age  from  year  to  year  (0.84  yr.),  and  the  smallest  increase  in 
average  grade  from  year  to  year.  The  other  relations  are 
varied. 

The  fact  of  the  variability  in  the  results  of  the  non-selected 
boys  stands  out.  The  irregularity  of  the  growth  of  the  various 
abilities,  and  the  fact  that  in  21%  of  the  cases  the  boys  of  one 
age  are  actually  lower  than  those  of  the  previous  age,  point  to 
the  conclusion  that  certain  allowances  will  have  to  be  made  for 
chance  variations.  It  is  not  possible  to  acccount  for  the  varia- 
tions in  growth  by  reference  to  the  relative  increase  in  average 
age  or  average  grade  from  year  to  year. 

The  results  of  the  165  non-selected  girls,  shown  in  italics  in 
the  first  seven  columns  of  table  13,  were  studied  in  the  same 
manner  as  the  results  of  the  boys.  60  differences  between  the 
percentage  performance  of  the  girls  of  each  age  and  those  of 
the  preceding  age  were  obtained.  These  differences  ranged  from 
— 2>2>7g  to  -f  50%,  the  median  being  7%  {Q=&%).  10  of  the 
deviations  (17%),  were  minus  values.  The  largest  deviations 
were  shown  in  the  tests  of  naming  60  words,  ( — 33%,  11  to  12), 
counting  stamps    ( — 20%,    9    to    10),    and    drawing    designs 


I 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  75 

( — 14%,  8  to  9).    The  remaining  7  minus  deviations  were  below 
10%. 

The  average  increases  in  the  percentage  passed  from  year  to 
year  are  as  follows, —  6  to  7=3.9%;  7  to  8:=i5%;  8  to  9= 
8.8%;  9  to  10=10.1%;  10  to  11^8.7%;  II  to  12=1.8%.  Both 
boys  and  girls  show  the  smallest  average  increase  in  the  percent- 
age passed  in  the  step  from  11  to  12,  and  the  magnitudes  of  the 
increases  agree  fairly  well  except  for  the  step  from  6  to  7.  The 
increase  of  the  7  year  girls  over  the  6  year  girls  is  3.9%,  the 
next  to  the  smallest  increase  of  one  age  group  over  any  preceding 
group.  The  7  year  boys,  however,  show  an  average  increase  of 
16.1%,  over  the  6  year  boys,  the  largest  increase  of  any  group 
of  boys  over  any  preceding  group.  It  will  be  difficult,  then,  to 
draw  conclusions  concerning  sex  differences  from  a  comparison 
of  the  6  year  boys  and  girls,  for  the  6  year  girls  are  either  a 
superior  selection  or  the  6  year  boys  are  an  inferior  selection 
if  the  character  of  these  groups  be  judged  by  the  comparison 
with  the  7  year  subjects.  The  same  comparison,  on  the  other 
hand,  might  indicate  that  the  7  year  girls  were  an  inferior  se- 
lection and  the  7  year  boys  a  superior  selection  from  the  general 
run.  It  is  only  possible  to  point  out  the  irregularity,  however,  it 
is  not  possible  to  show  the  cause  of  the  irregularity. 

A  comparison  of  the  average  increase  in  the  percentage  passed 
by  girls  from  age  to  age  with  the  increase  in  the  average  ages 
shown  in  Table  9  shows  no  demonstrable  relation  to  exist.  Com- 
paring this  growth  in  the  ability  on  the  tests  with  the  growth  in 
average  grade,  shown  in  Table  1 1 ,  shows  a  very  positive  relation 
to  exist  between  these  factors.  Where  the  increase  in  average 
grade  is  smallest  (i.e.  from  6  to  7  and  from  11  to  12),  the  in- 
crease in  the  tests  is  smallest  (3.9%  and  1.8%),  while  the  great- 
est increase  in  grade  (from  9  to  10  and  from  7  to  8)  coincide 
with  the  greatest  increase  in  the  test  abilities  (10.1%  and 
15.0%).  This  relation  was  not  indicated  in  the  results  of  the 
boys.  The  explanation  of  this  fact  that  a  correlation  between 
the  increase  in  the  tests  with  grade  was  found  in  the  results  of 
the  girls  but  not  of  the  boys  is  a  matter  of  speculation.  It  has 
been  shown  that  the  boys  have  a  higher  variability  in  grade  than 


Td  CARL  C.  B  RICH  AM    ■ 

girls.  This  tendency  of  the  boys  to  be  distributed  in  a  wider 
range  of  grades  might  nullify  the  grade  correlation  slightly, 
but  probably  not  to  any  considerable  extent.  The  fact  that  the 
causes  of  this  variation  are  not  determined  serves  to  illustrate 
the  dangers  of  comparing  the  results  of  two  groups  when  the 
factors  operating  on  the  groups  are  not  known. 

The  foregoing  study  of  the  growth  of  the  various  abilities 
from  age  to  age  in  each  sex,  and  the  analysis  of  the  causes  in- 
fluencing this  growth,  demonstrates  the  great  variability  of  the 
results.  This  fact  of  variability  must  be  considered  before  draw- 
ing conclusions  concerning  sex  differences  by  the  method  of 
comparing  the  results  of  boys  and  girls  of  each  age. 

The  percentage  differences  between  the  performance  of  non- 
selected  boys  and  girls  of  each  age  are  shown  in  Table  13.  In 
actual  magnitude,  these  differences  vary  from  0%  to  36%,  the 
median  being  9%  (Q^5.5%).  75%  of  the  differences  are 
17%  or  under,  and  only  16%  are  over  20%.  In  regard  to  sign, 
the  differences  vary  from  — 36%  to  -f-26%,  the  median  being 
— 3.5%  (Q=8.75%),  showing  a  slight  general  superiority  of 
the  girls.  If  the  number  of  possibilities  of  variation  in  compar- 
ing the  results  of  small  groups  of  non-selected  subjects  are 
taken  into  consideration,  the  presence  of  mental  defectives,  of 
subjects  having  language  difficulties,  of  subjects  in  different 
grades  influenced  by  different  training,  the  possibility  of  a  super- 
ior selection  of  subjects  at  one  age  group  than  at  another,  and  the 
probability  that  similar  chance  samplings  would  not  fall  at  the 
same  age,  the  fact  of  correspondence  indicated  in  Table  13  has 
more  meaning  than  the  fact  of  divergence. 

The  variability  indicated  in  the  study  of  the  growth  of  abilities 
with  age  was  so  great  that  it  makes  interpretation  of  the  results 
in  terms  of  sex  dift'erences  very  difficult,  and  warranted  conclu- 
sions impossible.  It  is  legitimate  to  expect  that  the  older  subjects 
of  either  sex  should  make  higher  scores  than  the  younger  sub- 
jects of  the  same  sex,  but  this  was  not  found  to  be  the  universal 
rule.  The  boys'  results  showed  minus  deviations  in  21%  of  the 
cases  and  the  girls'  results  showed  minus  deviations  in  17%  of 
the  cases.     In  one  case  the  12  year  girls  were  33%  lower  than 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  77 

the  II  year  girls.  If  this  value  (33%)  be  taken  as  the  error  due 
to  chance  variation,  then  only  one  value,  that  of  — 36%,  (naming 
the  months,  age  12),  may  be  taken  as  significant,  and  it  has  been 
seen  that  in  this  test  the  12  year  boys  are  10%  lower  than  the  9 
year  boys.  The  conclusion  would  follow,  then,  that  there  were 
no  sex  differences.  This  alternative,  however,  seems  to  place  too 
much  weight  on  one  variation  so  that  the  truth  probably  lies  in 
the  assertion  that  the  sex  differences,  that  actually  exist,  are 
slight. 

A  study  of  the  reactions  of  selected  groups  of  boys  and  girls 
should  throw  light  on  the  results  from  non-selected  subjects,  and 
make  conclusions  more  certain.  Subjects  were  selected  by  a 
process  of  elimination  and  selection.  All  of  the  subjects  that 
were  in  the  special  class  and  minus  grades  were  eliminated,  along 
with  all  children  of  non-English  speaking  parents.  From  the 
following  group  of  English  speaking  subjects  in  the  regular 
grades  all  subjects  were  eliminated  who  had  entered  grade  at  an 
age  very  much  above  or  below  that  of  the  general  run  of  en- 
trants.* The  remaining  subjects  ranged  in  age  from  4.3  years 
to  14.4  years,  but  were  found  to  group  rather  closely  around 
certain  ages.  It  was  possible  to  find  four  groups  of  boys  and 
girls  of  approximately  the  same  chronological  ages.  The  char- 
acter of  these  subjects  is  indicated  in  Table  14. 

The  four  groups  of  subjects,  chronologically  from  6.0  to  6.9, 
7.6  to  8.9,  9.7  to  10.9  and  11.7  to  13.3  (which  will  be  referred 
to  as  6,  8,  10  and  12),  were  distributed  in  approximately  the 
same  grades,  and  had  approximately  the  same  average  age  and 
average  grade.  The  results  of  these  groups  are  shown  in  Table 
15,  which  is  arranged  to  show  all  the  facts  for  selected  subjects 
that  were  given  for  non-selected  subjects  in  Tables  12  and  13. 
The  first  four  columns  show  the  percentage  that  each  test  was 
given  to  each  group.  The  next  four  columns  show  the  percentage 
or  the  proportion  that  the  subjects  in  each  group  passed  each 

*  The  ages  on  entering  each  grade  of  the  subjects  retained  were  as  fol- 
lows,— Kindergarten  —  4,  5  and  6;  Grade  I  =:  5,  6  and  7;  Grade  II  =  6,  7 
and  8;  Grade  III  =  8,  9  and  10;  Grade  IV  =  9,  10  and  11 ;  Grade  V  =  10, 
II  and  12;  Grade  VI  =  11,  12  and  13. 


78  CARL  C.  BRIGHAM 

TABLE  14 

Age  in  Grade  Distribution,  Average  Grade  and  Average  Age  of  167  Selected 

Subjects.    86  Boys  and  81  Girls. 

Age  in  Grade  Distribution 


Age  Group 

Sex 

K 

I 

II  III  IV 

V 

VI  TOTAL  Average 

Average 

Grade  (M.V.)  Age  (M.V.) 

6.0  to  6.9 

Boys 

5 

13 

18 

0.72  (0.40) 

6.52  (0.22) 

Girls 

3 

13 

2 

18 

0.89  (0.39) 

6.53  (0.22) 

7.6  to   8.9 

Boys 

7 

13     3 

23 

1.83  (0.51) 

8.09  (0.38) 

Girls 

2 

13     5 

20 

2.15  (0.43) 

8.32  (0.38) 

9.7  to  10.9 

Boys 

6 

12 

2 

20 

3.80  (0.48) 

10.37  (0.36) 

Girls 

9 

7 

5 

21 

3.8i  (0.69) 

10.14  (0.32) 

11.7  to  13.3 

Boys 

2 

8 

15 

25 

S.52  (0.58) 

12.35  (0.55) 

Girls 

3 

8 

II 

22 

5.36  (0.64) 

12.41  (0.46) 

test.  Column  A  shows  the  total  number  of  times  each  test  was 
given  to  all  boys  and  girls,  Column  B,  the  weighted  average  age 
(the  average  ages  given  in  Table  14  being  used),  and  Column  C 
the  percentage  that  all  subjects  passed  each  test.  The  next  four 
columns  show  the  percentage  that  the  boys  are  above  (  +  )  or 
below  ( — )  the  girls.  Column  D  (derived  from  Column  B), 
gives  the  difference  between  the  average  ages  of  all  subjects  to 
whom  each  test  was  given.  Column  E  (derived  from  Column 
C),  gives  the  differences  between  the  percentages  passed  by  all 
boys  and  girls  on  each  test. 

The  growth  of  the  various  abilities  with  age  in  the  selected 
groups  of  subjects  is  more  uniform  than  that  shown  by  the  non- 
selected  subjects.  Only  three  cases  appear  in  which  the  younger 
subjects  make  higher  scores  than  those  of  older  subjects,  these 
exceptions  occurring  in  the  tests  of  describing  pictures  ( — 3%, 
girls  6  to  8),  naming  colors  ( — 7%,  girls  6  to  8),  and  naming 
months  ( — 9%,  boys,  10  to  12).  In  the  comparison  of  the 
sexes  41  differences  are  obtained  varying  in  magnitude  from 
— 28%  to  +26%,  the  median  being  0%  {Q=g,^%).  In  actual 
magnitude  the  differences  vary  from  o  to  28,  the  median  being 
10%  (Q=4.75%),  the  median  being  1%  higher  than  that  of 
non-selected  data,  and  the  variability  0.75%  less.  75%  of  the 
differences  were  less  than  14%. 


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8o  CARL  C.  BRIGHAM 

The  change  of  the  median  of  the  series  of  differences  from 
— 3.5%  (non-selected)  to  0%  (selected)  shows  that  the  elimina- 
tion of  over  age  and  special  grade  pupils  has  helped  the  boys 
more  than  the  girls,  and  has  altered  the  general  relations  between 
the  sexes.  This  fact  is  also  indicated  by  the  average  difference 
in  the  percentages  that  all  subjects  pass  each  test,  the  average  for 
non-selected  subjects  being  — 1.4%  and  for  selected  subjects 
-f-i.6%.  The  non-selected  boys  from  6  to  12  were  given,  in  all, 
2436  tests,  these  tests  being  passed  60.8%  of  the  time.  The 
non-selected  girls  were  given  2195  tests,  passing  61.6%,  the 
advantage  being  0.8%  in  their  favor.  The  selected  boys  were 
given  1 125  tests,  passing  64.3%,  an  advantage  of  0.1%  over  the 
girls  who  passed  64.2%  of  1034  tests.  The  foregoing  changes 
indicate  clearly  that  the  selection  of  subjects  has  changed  the 
general  relations  between  the  sexes,  helping  the  boys  more  than 
the  girls. 

The  relations  between  the  results  of  selected  and  non-selected 
subjects  may  be  studied  by  a  comparison  of  the  differences  be- 
tween the  percentages  passed  by  all  subjects.  If  the  differences 
between  the  scores  of  the  boys  and  girls  are  due  to  but  one 
factor,  that  of  sex  differences,  then  the  correlation  between  the 
two  methods  of  study  should  be  very  nearly  absolute.  The  cor- 
relation (Pearson  product-moments  formula)  between  the  dif- 
ferences in  the  percentage  passed  by  all  boys  and  girls  according 
to  the  two  methods  is  0.726  (pe=o.o75).  This  correlation  be- 
tween the  two  methods  is  high,  but  it  would  probably  be  high 
inasmuch  as  the  167  selected  subjects  are  included  in  the  352 
non-selected  subjects.  The  results  of  the  two  methods  show  cer- 
tain large  discrepancies.  The  changes  of  the  greatest  magnitude 
are  those  shown  by  the  60  words  test  (+4%  by  the  first  method 
to  +  18%  by  the  second),  the  tests  of  defining  in  terms  superior 
to  use  (+7%  to  +21%),  of  naming  the  days  of  the  week, 
( — 16%  to  — 2%),  giving  rhymes,  ( — 10%  to  +1%),  naming 
colors,  ( — 14%  to  ' — 4%),  copying  the  diamond,  (  +  1%  to 
— 8%),  and  counting  from  20  to  o  ( — 8%  to  — 16%), 
The  comparison  of  the  median  differences  shows  that 
the  selected  method  tends  to  improve  the  results  of  the  boys  more 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  8i 

than  those  of  the  girls.  All  of  the  changes  in  the  results  of  the 
two  methods  are  not  in  favor  of  the  boys,  however,  the  total 
scores  on  the  diamond  and  20  to  o  tests  showing  changes  in 
favor  of  the  girls.  If  the  cause  of  the  variations  shown  by  the 
first  method  is  the  presence  of  a  few  children  of  non-English 
speaking  parents,  to  special  class  and  minus  grade  children,  then 
the  elimination  of  this  source  of  error  should  change  the  results 
in  only  one  direction. 

The  analysis  of  the  results  of  selected  subjects,  therefore,  does 
not  lessen  the  difficulty  of  the  interpretation  of  the  results  in 
the  light  of  sex  differences.  The  rate  of  growth  of  the  various 
abilities  with  age  is  irregular.  The  analysis  of  the  irregularities 
points  to  the  fact  that  the  boys  or  girls  of  any  age  may  be  a 
chance  selection  of  superior  or  inferior  subjects  at  that  age.  The 
method  of  comparing  selected  subjects  would  tend  to  eliminate 
the  inferior  selection  of  subjects,  but  would  not  eliminate  the 
possibility  of  a  superior  selection. 

The  comparison  of  the  results  of  the  sexes  shows  differences 
at  certain  ages  and  on  certain  tests  that  are  as  high  as  20%. 
The  problem  involved  is  that  of  deciding  whether  these  large 
differences  are  due  to  chance  or  to  differences  in  the  reactions 
of  the  sexes.  Certain  tests  show  large  deviations  first  in  favor 
of  one  sex  and  then  in  favor  of  the  other.  If  a  difference  of  a 
percentage  of  any  magnitude  on  any  test  is  to  be  attributed  to  a 
sex  difference,  then  the  same  line  of  reasoning  will  show  that  in 
certain  tests  the  abilities  change  from  one  sex  to  the  other.  The 
analysis  of  the  tests  that  show  this  crossing  of  ability  should 
throw  light  on  the  other  tests. 

Three  tests  show  substantial  differences  in  favor  of  both  sexes 
according  to  both  methods.  In  the  test  of  copying  the  diamond, 
the  non-selected  girls  lead  at  the  start,  age  6,  and  the  boys  are 
ahead  at  7,  8  and  9,  the  same  relations  being  shown  by  selected 
subjects  of  6  and  8.  In  the  test  of  copying  the  designs  from 
memory,  the  non-selected  girls  are  24%  below  the  boys  at  age  9 
and  21%  above  the  boys  at  age  12,  the  same  relations  being 
shown  by  the  selected  subjects  of  10  and  12.  In  the  test  of 
naming  60  words  in  three  minutes,  the  non-selected  girls  are 


82 


CARL  C.  B  RICH  AM 


19%  above  the  boys  at  9,  and  19%  below  at  12.     The  selected 
boys  of  10  and  12  are  in  advance  of  the  girls  in  this  test. 

These  three  tests  are  crucial  in  the  consideration  of  the  prob- 
lem of  whether  differences  shown  between  the  boys  and  girls  are 
due  to  actual  sex  differences  or  due  to  accidental  causes.  Each  of 
these  tests  may  be  studied  by  a  method  more  accurate  than  that  of 
comparing  the  percentage  passed  at  each  age.  The  reproductions 
of  the  diamond  were  arbitrarily  sorted  in  six  groups  according 
to  their  merits  by  a  method  described  in  the  discussion  of  the 
personal  equation.  The  first  group  contained  the  best  repro- 
ductions, the  sixth,  the  poorest.  The  reproductions  of  the 
designs  were  graded  from  o  to  20  by  an  arbitrary  point  system 
described  under  the  discussion  of  the  personal  equation.  A 
measure  of  the  ability  in  the  60  word  test  is  the  actual  number  of 
words  given  in  three  minutes,  a  measure  recorded  by  the  experi- 
menters in  each  case.  Table  16  shows  the  average  score  made 
by  the  non-selected  and  selected  boys  and  girls  of  each  age  in 
these  three  tests. 

TABLE  16 
Average  Score  (Mean  Variation)  of  Subjects  of  Each  Age  on  Three  Tests. 


Copying  the  Diamond 
Average  Group  of 
the  Reproductions, 
en  Boys  Girls 

!_  6  4.27(1.28)  3.57(1.24) 
^  7  2.85(1.04)  3.17(1-37) 
^    8   2.20(1.15)  3.24(1.57) 

^    9    2.33(0.89)  3.00(1.29) 
u 
^  10 

-  II 

=   12 

•«^    6  4.27(1.20)  3.33(1.26) 
u.H.   8  2.32(1.00)  3.00(1.17) 


Drawing  the  Designs 

Average  number  of 

points  scored. 


Boys 


Girls 


8.06(6.19)  9.00(5.25) 
10.29(5.30)  5.32(4.61) 
9.I7(S.33)  9.18(6.73) 
8.64(6.73)  10.94(7.06) 
8.64(6.02)  11.08(6.08) 


9.55(5.60)    7.29(6.42) 
12.53(5.38)  13.56(5.55) 


Naming  60  words 
Average  number  of  words 
given  in  three  minutes. 
Boys  Girls 


52.93(11.20)  59.91(10.10) 

68.12(13.12)  61.76(11.25) 

73.65(13.35)  71.28(14.25) 

68.75(12.28)  58.14(12.57) 


67.31(12.74)  62.13(11.39) 
75.33(10.92)  66.84(13.87) 


The  relations  indicated  by  the  percentage  passed  are  also  indi- 
cated by  the  more  reliable  method  of  comparing  the  average 
scores.  In  the  test  of  copying  the  diamond,  the  6  year  non- 
selected  girls  average  0.70  group  better  than  the  boys,  while  the 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  83 

selected  girls  are  0.94  ahead.  The  comparison  of  the  7,  8  and  9 
year  subjects  shows  the  boys  ahead  in  all  cases,  the  8  year  non- 
selected  boys  averaging  over  one  group  higher.  The  non-selected 
boys  show  an  improvement  of  two  groups  from  6  to  9,  while  the 
girls  show  an  improvement  of  only  half  a  group.  One  sex  shows 
a  decided  growth  of  ability,  the  other  practically  none.  If  the 
differences  indicated  are  to  be  taken  as  real,  it  will  be  necessary 
to  assume  that  the  girls  pick  up  the  ability  to  draw  a  diamond 
easier  than  the  boys,  but  that  this  ability  once  obtained  remains 
constant — that  the  effect  of  maturity  operates  on  one  sex  but 
not  on  another.  The  number  of  cases  on  which  this  assumption 
is  based  (174  subjects  from  6  to  9)  is  so  small,  and  the  chances 
of  variation  in  the  selection  of  subjects  of  different  intellectual 
status  in  each  age  group  is  so  large,  that  the  assumption  is  not 
substantiated. 

The  relations  indicated  in  the  test  of  copying  the  designs  are 
more  variable  than  those  of  the  diamond  test.  The  9  year 
non-selected  boys  show  an  improvement  over  the  8  year  boys,  but 
from  9  to  12  there  is  a  gradual  decrease  in  the  ability,  so  that 
the  1 1  and  12  year  boys  are  only  slightly  ahead  of  the  8  year  boys. 
The  relations  shown  by  the  non-selected  girls  are  exactly  the 
reverse  of  those  of  the  boys.  The  9  year  girls  are  very  much 
lower  than  the  8  year  girls,  and  a  gradual  increase  appears  from 
9  to  12  instead  of  a  decrease.  The  comparison  of  these  opposite 
relations  gives  a  maximum  difference  in  favor  of  the  boys  at  9 
and  the  girls  at  12.  If  the  relations  indicated  in  this  test  are  to  be 
considered  definite,  the  assumption  is  involved  that  the  influence 
of  increasing  age  on  one  sex  is  exactly  opposite  to  that  on  the 
other  sex,  an  assumption  that  is  not  substantiated  in  view  of  the 
small  number  of  cases  (183  subjects  from  8  to  12)  and  the  possi- 
bility of  selecting  subjects  of  chance  superiority  in  the  small 
groups  at  each  age. 

The  relations  indicated  in  the  test  of  naming  60  words  are 
more  constant  than  those  shown  in  the  diamond  or  design  tests. 
Both  sexes  show  a  growth  of  ability  from  9  to  11  and  a  decrease 
from  II  to  12.  The  growth  is  irregular,  however,  the  girls 
showing  less  growth  from  9  to  10,  and  a  greater  drop  from  11  to 


84  CARL  C.  BRIGHAM 

12,  SO  that  a  comparison  of  the  sexes  shows  a  deviation  in  favoi 
of  the  girls  at  9  and  of  the  boys  at  12.  The  assumption  of  any 
large  sex  differences  in  this  test  involves  the  assumption  that  12 
year  girls  have  less  ability  in  this  test  than  9  year  girls,  and  that 
the  influence  of  maturity  operates  differently  on  the  two  sexes, 
an  assumption  that  is  not  substantiated  in  view  of  the  many  varia- 
ble factors. 

The  conclusion  that  a  definite  crossing  of  ability  between  the 
sexes  occurs  in  the  tests  of  copying  the  diamond,  copying  designs 
and  naming  60  words,  is  not  substantiated.  It  is  not  justifiable 
to  attribute  a  difference  of  20%  between  the  sexes  to  a  real  sex 
difference  on  one  test  and  not  on  another.  If  the  differences 
shown  between  the  results  of  the  sexes  in  the  tests  of  constructing 
a  sentence  containing  one  idea,  of  naming  the  months,  naming 
the  days  of  the  week,  counting  stamps  and  naming  colors  are 
to  be  attributed  to  sex  differences,  then  the  variations  in  ability 
shown  in  the  diamond,  design  and  60  word  test  must  be  assumed 
to  be  definite.  These  assumptions  were  not  found  to  be  sub- 
stantiated, however,  so  that  it  is  not  possible  to  draw  any  con- 
clusions concerning  sex  differences  from  a  study  of  the  percent- 
age that  selected  or  unselected  subjects  of  each  age  pass  each 
test. 

The  variable  influences  due  to  the  selection  of  subjects  of 
different  status  at  each  age  are  eliminated  or  counterbalanced  to 
some  extent  by  combining  the  subjects  of  all  ages.  The  differ- 
ences between  the  percentages  that  all  boys  and  girls  pass  each 
test  are  to  some  extent  influenced  by  the  ages  of  the  subjects  to 
whom  each  test  was  given.  The  correlation  (Pearson  product- 
moments  formula)  of  the  differences  between  the  percentages 
that  all  non-selected  boys  and  girls  passed  each  test  with  the 
difference  between  the  average  ages  of  all  the  non-selected  boys 
and  girls  to  whom  each  test  was  given  is  0.394  (pe=o.i34).  The 
correlation  between  the  same  arrays  from  selected  subjects  (i.e. 
between  Columns  D  and  E  of  Table  15)  is  0.388  (pe=o.i35). 
These  correlations  between  the  tests  and  age  are  high  enough  to 
indicate  that  the  factor  of  age  is  present  to  some  extent.  The 
close  correspondence  in  the  correlations  from  the  two  methods 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  85 

indicates  that  the  age  factor  is  present  to  the  same  extent  in  both 
methods.  The  tests  vary  in  the  degree  with  which  they  correlate 
with  age,  so  that  it  is  not  possible  to  estimate  the  amount  of  the 
influence  of  this  factor.  Furthermore,  it  has  been  seen  that  the 
results  from  the  two  methods  are  not  in  strict  accordance,  that 
the  elimination  of  inferior  subjects  caused  changes  in  the  results 
in  both  directions.  For  these  reasons,  it  is  not  possible  to  draw 
any  conclusions  concerning  sex  differences  from  a  comparison 
of  the  percentages  passed  by  all  subjects. 

Certain  negative  conclusions  are,  however,  possible.  The  num- 
ber of  subjects  at  each  age  in  both  methods  is  comparatively 
small.  The  chances  of  variations  due  to  factors  other  than  sex 
differences  has  been  shown  to  be  very  large.  The  fact  of  corres- 
pondence between  the  results  of  the  two  sexes  is  therefore  of 
more  importance  than  the  fact  of  divergence.  75%  of  the  differ- 
ences between  the  non-selected  boys  and  girls  are  17%  or  under, 
while  the  same  proportion  of  the  differences  between  selected 
boys  and  girls  falls  under  14%.  If  it  is  assumed  that  the  subjects 
of  any  age  should  not  test  lower  than  those  of  any  preceding  age, 
and  allowance  is  made  for  differences  between  the  sexes  that  are 
exaggerated  on  account  of  the  chance  falling  off  of  ability  with 
older  subjects,  only  9%  of  the  differences  between  the  non- 
selected  boys  and  girls  are  over  20%  (derived  from  Table  13). 

The  evidence  from  the  foregoing  methods  of  study  points  to 
the  conclusion  that  the  sex  differences,  if  present,  are  under  20% 
or  25%  as  a  maximum,  and  that  deviations  of  this  magnitude 
are  marked  exceptions  to  the  general  run  of  differences.  The 
conclusion  that  the  differences  that  might  possibly  be  attributed 
to  the  sex  factor  are  slight,  has  no  meaning  unless  the  word 
"slight"  is  defined  independently  of  the  writer's  personal  opinion. 
The  differences  shown  between  the  results  of  the  sexes  are 
smaller  than  those  that  were  attributed  to  the  factor  of  the  per- 
sonal equation  in  the  study  of  the  results  of  the  four  experi- 
menters. It  was  concluded  that  certain  tests  were  influenced  by 
grade  training.  These  tests  showed  from  40%  to  60%  improve- 
ment from  one  grade  to  another,  so  that  the  greatest  influence 
that  may  be  attributed  to  the  sex  factor  is  only  approximately 


86  CARL  C.  BRIGHAM 

one  half  that  due  to  grade  training.  The  following  study  of  the 
diagnostic  value  of  the  tests  will  show  that  the  deviations  that 
might  be  attributed  to  the  sex  factor  are  insignificant  when  com- 
pared to  the  differences  between  the  reactions  of  normal  and  re- 
tarded children  to  the  individual  tests. 

Most  of  the  investigators  who  have  studied  the  factor  of  sex 
differences  in  the  Binet  tests,  have  studied  them  from  the  stand- 
point of  the  "mental  ages"  or  total  scores  made  by  the  subjects 
of  both  sexes.  A  few  investigators  have  studied  sex  differences 
in  the  light  of  the  individual  tests.  Descoeudres  (20)  reports  the 
results  of  the  application  of  the  Binet  tests  to  24  subjects,  one 
good  and  one  poor  pupil  of  each  sex  from  each  of  six  school 
grades,  drawing  conclusions  from  this  investigation  concerning 
the  diagnostic  value  of  the  individual  tests  and  the  sex  differences 
involved.  Obviously  the  number  of  subjects  is  too  small  to 
allow  any  conclusions  to  be  drawn.  Chotzen  (18)  compared  the 
percentage  that  all  feeble-minded  boys  and  girls  passed  each  of 
15  tests,  finding  differences  varying  in  magnitude  from  1%  to 
20%.  The  largest  deviations  were  those  of  20%  in  favor  of 
the  boys  in  the  test  of  copying  the  diamond,  13%  in  favor  of  the 
girls  in  the  test  of  executing  three  commissions,  12%  in  favor 
of  the  boys  in  naming  the  pieces  of  money,  ii%>  in  favor  of  the 
girls  in  the  test  of  repeating  a  sentence  of  16  syllables,  and  10% 
in  favor  of  the  girls  in  detecting  omissions  in  pictures.  All  other 
differences  were  less  than  10%. 

Bloch  and  Preiss  (9)  examined  155  normal  Volkschule  chil- 
dren (79  boys  and  76  girls)  varying  in  age  from  7  to  13.  Bober- 
tag's  translation  was  used.  These  investigators  found  very  strik- 
ing differences  in  the  reaction  of  the  sexes  to  the  individual  tests, 
the  differences  running  as  high  as  52%,  most  of  them  in  favor 
of  the  boys.  The  differences  between  the  performances  of  the 
boys  and  girls  of  each  age  were  calculated,  without  reference  to 
the  many  sources  of  variation.  The  factor  of  the  personal  equa- 
tion is  not  treated,  and  this  factor  alone  might  cause  these  varia- 
tions. If  a  more  careful  analysis  of  the  results  had  been 
made,  it  is  very  probable  that  the  conclusions  would  have 
been  modified  to  some  extent.      The    fact    that    the    11    year 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  87 

boys  are  37%  higher  than  the  11  year  girls  on  the  test 
of  criticising  absurdities  is  most  certainly  modified  by  the 
fact  that  the  11  year  subjects  are  30%  lower  than  the  10 
year  subjects  in  the  test  of  repeating  7  digits.  The  small  num- 
ber of  subjects  (in  five  cases  less  than  10),  would  tend  to  empha- 
size chance  variations.  The  fact  that  the  number  of  subjects  is 
too  small  to  warrant  definite  conclusions  is  pointed  out  by  the 
authors.  Stern  (62)  in  commenting  upon  these  results,  points 
out  the  significance  of  the  fact  that  the  inferiority  of  the  girls 
extends  to  so  many  different  kinds  of  tests.  The  results  of 
Bloch  and  Preiss  are  in  almost  complete  contradiction  to  the  re- 
sults of  the  present  investigation.  They  find  large  differences, 
and  find  practically  all  of  these  differences  in  favor  of  the  boys. 
This  investigation  shows  a  general  run  of  differences  very  much 
smaller,  and  a  slight  general  superiority  of  the  non-selected  girls. 
The  mere  fact  of  contradiction  in  the  results  of  the  two  investiga- 
tions would  indicate  that  the  differences  were  not  produced  by 
the  common  factor  of  sex.  Rogers  and  Mclntyre  (54)  give  no 
figures,  but  report  that  they  have  studied  their  results  in  the  light 
of  sex  differences,  and  have  found  no  correlation  between  their 
results  and  those  of  Bloch  and  Preiss. 

The  results  of  the  investigators  who  have  compared  the  "men- 
tal ages"  or  total  scores  of  children  of  different  sexes  are  some- 
what at  variance.  Goddard  (30)  reports  that  there  are  more 
backward  boys  than  girls.  Stern  notes  that  Goddard's  results 
do  not  bear  out  his  statement,  for  the  percentage  of  boys  and 
girls  testing  two  or  more  years  retarded  is  the  same  (18.5%). 
The  accuracy  of  Goddard's  statement  depends  on  the  criterion' 
used  for  measuring  backwardness.     Although  Goddard's  state- 

^  If  the  criterion  is  four  or  more  years  retarded,  there  are  more  backward 
boys  than  girls  (boys  =  3.7%,  girls  =:  3.1%).  If  the  criterion  is  three  or 
more  years  backward,  there  are  more  girls  than  boys  (boys  :=  S%, 
girls  =  9.1%).  If  the  criterion  is  two  or  more  years  backward,  the  propor- 
tions are  the  same,  as  Stern  notes.  If  the  criterion  is  one  year  or  more  re- 
tarded, there  are  more  backward  boys  than  girls  (boys  =  41.4%,  girls  = 
35-6%).  There  are  more  girls  than  boys  testing  at  and  above  age  according 
to  Goddard's  results.  34.7%  of  the  boys  and  36.6%  of  the  girls  test  at  age, 
while  23.8%  of  the  boys  and  27.7%  of  the  girls  test  one  year  or  more  above 
age. 


88  CARL  C.  BRIGHAM 

ment  concerning  the  backwardness  of  the  boys  may  be  interpreted 
differently,  his  figures  leave  no  doubt  concerning  the  fact  that 
there  are  more  girls  than  boys  at  and  above  age,  and  therefore 
indicate  a  general  superiority  of  the  girls. 

Bobertag  (lo)  computed  the  average  "mental  age"  of  90  boys 
and  90  girls  regularly  distributed  from  7  to  12.  The  subjects 
were  selected  according  to  school  grades,  so  that  the  average 
grade  of  each  group  differed  by  exactly  one  grade.  His  results 
show  the  boys  ahead  0.06  yr.  at  7,  0.14  yr.  at  8  and  9,  0.20  yr. 
at  10,  0.19  yr.  at  11  and  0.14  yr.  at  12.  These  findings  cannot 
be  considered  entirely  out  of  harmony  with  those  of  Goddard, 
for,  as  this  investigation  shows,  there  may  be  a  change  in  the 
relation  of  non-selected  boys  and  girls  and  selected  boys  and  girls. 

Yerkes  and  his  co-workers  (82),  scoring  some  of  the  Binet 
tests  according  to  the  point  system,  show  that  the  girls  of  English 
speaking  parents  are  superior  to  the  boys  of  the  same  parentage 
between  5  and  7,  that  they  fall  below  with  minor  variations  till 
II,  where  they  again  surpass  the  boys  at  12  and  13,  falling  below 
at  14  and  15.  The  differences  between  the  sexes  are  smaller 
and  of  less  practical  importance  than  the  differences  due  to  the 
language  factor,  but  the  authors  suspect  "that  at  certain  ages 
serious  injustice  will  be  done  to  individuals  by  evaluating  their 
scores  in  the  light  of  norms  which  do  not  take  account  of  sex 
differences."  (page  73).  In  contradiction  to  these  results  are 
those  of  Terman  and  his  co-workers  (67),  who,  scoring  the 
Stanford  revision  of  the  Binet  scale  according  to  "intelligence 
quotients,"  find  differences  of  but  2%  to  4%  in  these  quotients 
in  favor  of  the  girls,  and  who  conclude  from  the  basis  of  their 
studies  of  sex  differences  that  the  conclusions  of  Yerkes  are 
unjustified.  These  two  investigations  used  tests  different  in 
character  and  differently  weighted,  so  that  the  results  would  not 
necessarily  have  to  correspond. 

The  one  common  feature  of  most  of  the  researches  on  sex 
differences  in  the  Binet-Simon  tests  is  that  the  differences  are 
small.  Burt  and  Moore  (17)  summarize  the  work  of  various  in- 
vestigators in  the  general  field  of  sex  differences,  and  report  an 
investigation  of  their  own  on  67  boys  and  63  girls,  12^  to  13^^ 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  85 

years  of  age.  They  discuss  their  results  and  those  of  the  other 
authors  in  the  order  of  the  complexity  of  the  mental  processes 
involved.  They  find  a  high  correlation  between  the  size  of  the 
sex  difference  and  the  simplicity  of  the  capacities  compared — the 
higher  the  process,  and  the  more  complex  the  capacity,  the 
smaller  the  sex  difference. 

The  general  trend  of  the  investigations  on  sex  differences  indi- 
cates that  no  very  large  differences  are  to  be  expected  in  the 
application  of  intelligence  tests,  and  that  the  differences  to  be 
expected  will  vary  according  to  the  nature  of  the  tests.  The  re- 
sults of  this  investigation  are  in  agreement  with  the  general 
trend  of  the  investigations  in  showing  only  slight  differences  that 
might  be  attributed  to  the  sex  factor.  The  results  do  not  show 
on  what  tests,  if  any,  these  differences  occur.  Conclusions  con- 
cerning the  amount  of  influence  of  this  factor  must  be  drawn 
from  more  exhaustive  investigations  on  the  individual  tests.  The 
research  of  Bateman  (3),  for  instance,  is  conclusive  in  the  test 
of  naming  colors.  Bateman  shows  that  there  is  a  difference  of 
14%  in  favor  of  the  girls  in  this  test,  showing  furthermore  that 
the  factor  of  school  training  causes  an  improvement  of  but  18%. 
The  results  would  indicate  that  the  test  should  be  placed  in  the 
fifth  or  sixth  year,  but  the  sex  dift'erence  of  14%  would  probably 
not  warrant  the  placing  of  the  test  in  a  different  age  group  for 
boys  and  girls. 

The  investigations  of  Bolton  (11)  and  Wooley  (79)  would 
show  that  small  differences  in  favor  of  the  girls  are  to  be  ex- 
pected in  the  tests  of  repeating  digits,  and  possibly  in  all  memory 
tests.  The  investigations  of  Gilbert  {2y),  Thompson  (68), 
Burt  and  Moore,  and  Peterson  and  Doll  (51)  would  indicate  that 
a  slight  difference  in  favor  of  the  boys  should  appear  in  the  test 
of  arranging  five  weights.  Ruger's  (55)  finding  of  striking  dif- 
ferences in  favor  of  men  in  a  series  of  puzzle  tests,  and  Wooley 
and  Fisher's  finding  of  large  differences  in  favor  of  the  boys  in 
the  Healy  puzzle-box  test  would  show  that  rather  large  differ- 
ences might  appear  in  the  general  class  of  "puzzle"  tests. 

Even  though  the  sex  differences  in  intelligence  tests  may  be 
shown  to  be  small,  scientific  procedure  should  demand  that  the 


90  CARL  C.  BRIGHAM 

investigator  who  standardizes  any  test  or  system  of  tests  should 
treat  his  results  in  such  a  way  as  to  demonstrate  that  the  factor 
is  present  or  not  present.  The  burden  of  proof  should  still  be 
on  the  person  who  maintains  that  sex  differences  are  not  involved. 
The  knowledge  of  sex  differences  is  especially  important  in  diag- 
nosing border-line  cases  of  mental  defect,  where  the  diagnosis 
must  often  be  made  on  the  qualitatively  different  character  of 
the  responses  to  individual  tests. 


VI.     SUMMARY. 

One  of  the  fundamental  assumptions  in  the  construction  of  the 
Binet-Simon  scale  is  the  correlation  of  the  individual  tests  with 
age.  The  correlation  of  the  tests  with  age  is  affected  by  the 
error  due  to  incomplete  data,  by  the  influence  of  the  personal 
equation  of  the  experimenter,  and  by  the  training  the  subject  has 
received  in  school. 

The  influence  of  the  personal  equation  of  the  experimenter  was 
found  to  be  more  marked  in  some  tests  than  in  others,  the  in- 
fluence being  most  marked  in  the  tests  of  copying  the  diamond, 
indicating  omissions  in  pictures,  defining  in  terms  superior  to 
use,  drawing  designs  from  memory,  detecting  absurdities  in  state- 
ments and  reconstructing  dissected  sentences. 

The  variations  between  the  experimenters  could  be  traced  to 
three  sources, — 

1 )  to  the  use  of  apparatus,  variations  In  which  were  due  to, 

a)  the  construction  of  the  test  material,  and 

b)  the  use  of  alternative  questions; 

2)  to  the  technique  of  the  experimenters  in  giving  the  tests; 
and 

3)  to  observation  errors  made  by  the  experimenters  in  mark- 
ing a  response  passed  or  failed. 

It  is  possible  to  eliminate  all  three  sources  of  error. 

The  effect  of  school  training  was  more  marked  on  some  tests 
than  on  others,  the  effect  being  most  marked  in  the  tests  of  count- 
ing stamps,  counting  backward  from  20  to  o,  enumerating  the 
days  of  the  week  and  the  months,  giving  the  day  and  the  date, 
naming  the  pieces  of  money,  making  change,  and  reconstructing 
dissected  sentences.  Tests  that  involve  school  training  should  be 
standardized  on  a  different  basis  than  those  relatively  independent 
of  this  factor. 

Although  the  comparison  of  "mental  ages"  and  pedagogical 
ages  gives  no  information  concerning  the  general  correlation  be- 


92 


CARL  C.  B  RICH  AM 


tween  the  Binet  tests  and  the  school  grades,  the  study  of  the 
individual  tests  establishes  the  fact  of  a  general  correlation. 

The  correlation  of  the  individual  tests  with  grade  is  higher 
than  the  correlation  of  the  tests  with  age,  this  fact  being  indirect 
evidence  of  the  value  of  the  tests  as  measures  of  intelligence. 

Sex  differences  were  found  to  be  slight  as  compared  with  the 
influence  due  to  the  personal  equation  or  grade  training. 

Since  variations  occur  in  the  results  due  to  the  influence  of  the 
personal  equation  and  grade  training,  certain  allowances  must 
be  made  for  these  factors  in  making  diagnoses  on  the  basis  of 
the  tests.  The  scale  is  therefore  a  qualitative  rather  than  a  quan- 
titative instrument. 

The  investigator  who  wishes  to  use  his  results  for  standard- 
izing age  norms  should  use  only  those  data  based  on  the  com- 
plete method  of  experimenting,  and  should  treat  his  results  in 
such  a  Avay  as  to  demonstrate  the  presence  or  absence  of  the 
variable  factors  of  the  personal  equation,  grade  training  and  sex 
differences. 


■ifciiyyLiii—  .-11.  «i  .I'M 


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40  CARL  C.  B  RICH  AM 

studied.  The  use  of  the  normal  grade  age  as  a  measure  of 
scholastic  ability  is  false  inasmuch  as  it  rests  on  the  assumption 
that  all  children  enter  school  at  a  certain  age,  which  is  not  the 
case.  The  measure  of  scholastic  ability  is  the  measure  of  the 
child's  reaction  to  the  subject  matter  of  the  grades,  and  that 
measure  may  be  expressed  only  in  the  fact  of  promotion,  non- 
promotion  or  (very  rarely)  double  promotion,  in  other  words, 
it  may  be  expressed  only  in  the  relation  of  grade  to  the  length 
of  time  in  school.  Furthermore,  the  two  measures  of  scholastic 
ability,  the  age  in  grade  method,  and  the  grade  progress  method, 
are  measures  of  an  historically  past  performance  not  of  present 
possibilities,  and  the  true  measure  of  an  ability  must  indicate 
potential  ability. 

As  measures  of  scholastic  ability  in  terms  of  actual  reaction, 
these  measures  present  a  distribution  of  general  ability  that  is 
skewed  toward  the  lower  end,  or  in  the  direction  of  no  ability. 
If  a  child  enters  school  late,  he  presents  a  picture  of  retardation 
according  to  the  age  and  grade  method,  while  throug<h  any  num- 
ber of  causes  independent  of  intellectual  ability,  a  child  may 
present  a  retardation  of  at  least  a  year  according  to  either  method. 
The  possibilities  for  advancement  are  not  as  great,  however,  for 
advancement  means  forcing  a  child  through  a  mass  of  subject 
matter,  a  process  which  the  school  is  generally  unwilling  to 
undertake  and  the  parent  is  generally  unwilling  to  sanction.  The 
school  therefore  presents  a  picture  of  ability  in  which  promotion 
is  normal,  and  non-promotion  far  more  frequent  than  advance. 
If  general  ability  is  to  be  considered  as  distributed  over  any  sort 
of  a  frequency  surface,  that  surface  will  not  take  the  form 
presented  by  the  school  measure  in  which  the  modal  ability  is 
almost  completely  the  upper  limit. 

The  measure  of  "mental  age"  has  been  shown  to  be  one  which 
varies  from  one  chronological  age  to  another  in  the  form  of  its 
distribution.  Normal  children  of  6  or  7  test  over  age,  while 
those  of  II  and  12  test  under  age.  This  abnormal  distribution 
is  due  to  two  facts.  In  the  first  place,  the  tests  in  the  younger 
years  are  too  easy  and  those  in  the  higher  years  are  too  difficult. 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  41 

In  the  second  place,  the  younger  children  have  a  wider  range 
of  tests  beyond  their  average  ability,  so  that  exceptional  sub- 
jects may  display  exceptional  ability  in  a  manner  that  is  im- 
possible if  ability  is  measured  by  school  progress,  while  older 
children  have  only  a  few  tests  within  their  range,  the  picture 
of  advancement  being  excluded  as  in  the  measure  of  school 
ability.  If  the  mental  ages  of  a  run  of  subjects  of  different 
chronological  ages  are  combined,  the  frequency  surface  is  nor- 
mal, the  error  of  the  extremities  balancing. 

The  investigators  who  have  compared  "mental  age''  with  grade 
age,  have  compared  two  distributions,  one  of  which  is  markedly 
skewed,  the  other  normal,  but  false.  The  resulting  finding  of 
mental  advance  in  excess  of  pedagogical  advance  has  significance 
only  insofar  as  it  shows  that  a  measure  of  general  ability  that 
will  admit  of  exceptionally  high  performance  is  a  better  measure 
than  one  that  precludes  the  possibility  of  such  performance.  The 
only  significant  finding  is  that  pupils  w^ho  show  marked  retarda- 
tion in  school  rarely  if  ever  show  mental  advance. 

Applying  the  foregoing  discussion  to  Schmitt's  results  in  par- 
ticular, all  that  has  been  said  concerning  the  inadequacy  of  the 
age  in  grade  method  applies  to  her  results.  The  age  for  enter- 
ing school  being  5,  none  of  the  subjects  in  the  Kindergarten  could 
be  advanced,  while  those  who  entered  late  would  be  retarded. 
It  is  difficult  to  see  how  these  young  children  would  be  able  to 
make  up  their  work  in  such  a  way  as  to  show  advance  during  the 
first  two  or  three  school  years.  The  normal  age  for  the  sixth 
grade  is  from  11.5  to  12.5  years.  Inasmuch  as  no  grades  were 
tested  above  VI,  none  of  the  37  subjects  from  11.5  to  14.5  could 
show  an  advance,  and  all  of  the  19  subjects  from  12.5  to  14.5 
would  necessarily  show  retardation.  Schmitt's  results  dififer 
from  those  of  other  investigators  in  finding  more  subjects  ad- 
vanced according  to  Binet  age  in  relation  to  chronological  age. 
This  deviation  is  probably  due  to  the  fact  that  she  examined  a 
superior  selection  of  subjects,  and  to  the  fact  that  the  XV  year 
and  "Adult"  tests  were  used,  so  that  the  older  subjects,  who  in 
general  fall  below  their  chronological  age,  had  an  opportunity  to 


42  CARL  C.  BRIGHAM 

better  their  scores.  The  discrepancy  shown  hy  Schmitt  between 
school  standing  and  the  Binet  tests  does  not  demonstrate  the 
inadequacy  of  the  tests. 

The  final  demonstration  of  a  correlation  between  the  Binet 
scale  and  school  grade,  rests  not  in  comparing  the  total  score  or 
"mental  age"  with  school  grade,  for  that  is  susceptible  to  the 
errors  of  over-estimation  and  under-estimation  according  to  vary- 
ing chronological  age,  but  in  comparing  the  results  of  subjects 
in  each  grade  on  the  individual  tests.  The  tests  may  vary  in 
their  correlation  with  grade.  Inasmuch  as  there  is  a  general 
growth  in  age  with  grade,  and  a  corresponding  growth  of  in- 
telligence with  age,  a  test,  in  order  to  be  an  adequate  test  of 
intelligence,  must  show  a  correlation  with  grade.  If  the  correla- 
tion is  too  high,  however,  the  value  of  the  individual  test  is  in 
question  for  it  would  then  be  testing,  not  intelligence,  but  grade 
training.  This  criterion  was  actually  used,  though  not  stated, 
by  Binet  in  his  discussion  of  the  results  of  Decroly  and  Degand 
(19),  and  in  his  revision  of  the  1908  scale,  in  which  many  of 
the  tests  that  he  considered  to  relate  to  school  training  were 
eliminated. 

Studies  of  the  individual  tests  in  the  light  of  school  grade  are 
not  available.  Decroly  and  Degand  published  in  1910  the  re- 
sults of  an  investigation  on  45  children  in  a  Brussels  school, 
similar  in  character  to  that  studied  by  Schmitt  in  Chicago.  Binet 
discussed  these  results  and  those  of  other  minor  investigations  in 
the  Paris  schools  in  considering  the  effect  of  environment  on 
the  results  of  the  tests.  Although  he  referred  to  school  training 
as  a  factor,  and  classified  the  tests  in  which  Decroly  and  Degand's 
subjects  were  superior,  he  gave  no  quantitative  demonstration  of 
the  effect  of  this  factor.  The  results  of  Decroly  and  Degand 
are  based  on  too  few  subjects  to  admit  of  quantitative  treatment. 
Chotzen  (18)  studied  the  tests  by  comparing  the  performance  of 
feeble-minded  individuals  of  the  same  mental  age  but.  of  different 
chronological  age.  Although  this  method  shows  the  effect  of 
environment  and  maturity  on  feeble-minded  individuals,  it  does 
not  bear  directly  on  the  factor  of  school  training.     The  foregoing 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  43 

investigations  will  be  discussed  in  this  chapter  only  in  their 
relation  to  the  results  of  the  particular  tests.  Schmitt,  in  her 
monograph,  published  tables  showing  the  reaction  of  each  sub- 
ject in  each  grade  to  each  test,  the  tables  being  discussed  in  the 
text.  Although  it  was  not  Schmitt's  purpose  to  determine  the 
correlations  between  the  various  tests  and  grade,  her  data  are 
available  for  a  study  of  this  sort,  and  the  writer  has  taken  the 
liberty  of  figuring  them  in  this  light,  indicating  at  the  same  time 
Schmitt's  interpretation  of  the  grade  factor,  contained  in  the 
accompanying  text.  These  data  will  be  compared  with  the  re- 
sults of  the  Princeton  investigation. 

422  subjects  of  this  investigation  were  distributed  in  the 
kindergarten,  first  six  regular  grades,  minus  grades  and  the 
special  class  of  the  Princeton  Model  School.  301  of  the  subjects 
(161  boys  and  140  girls)  were  in  the  kindergarten  and  first  six 
regular  grades.  The  data  obtained  from  the  examination  of 
these  301  subjects  were  classified  according  to  the  grade  in  which 
the  subjects  were  found,  and  the  percentage  that  the  subjects 
of  each  grade  passed  each  test  was  calculated. 

Only  those  tests  were  studied  which  showed  themselves  to  be 
free  from  the  influence  of  the  personal  equation  of  the  four  ex- 
perimenters. The  elimination  of  the  unrecorded  results  of  the 
definitions  test  left  a  number  of  cases  too  small  to  be  studied.  To 
avoid  the  influence  of  the  error  due  to  incomplete  data,  the 
writer  has  calculated  the  percentage  from  only  those  tests  that 
were  given  from  75%  to  100%  of  the  possible  number  of  times. 
The  data  from  the  tests  of  repeating  5,  6  and  7  digits  have  been 
combined  into  one  weighted  measure.  The  procedure  of  the 
experimenters  in  giving  these  tests  was  to  start  within  the  sub- 
ject's range  and  continue  till  he  failed.  If  5  digits  were  suc- 
cessfully repeated,  6  were  given,  and  if  these  were  passed,  7  were 
given.  The  results  have  been  combined  into  one  measure  for  the 
sake  of  simplicity,  i  point  being  allowed  for  the  successful 
repetition  of  5  digits,  2  points  for  6  digits  and  3  points  for  7 
digits,  the  weighting  being  roughly  in  accordance  with  the 
weighting  in  Goddard's  scale,  the  tests  being  in  the  age  groups 


44  CARL  C.  B  RICH  AM 

VIII,  X  and  XII  respectively.  The  measure  of  the  ability  of  a 
group  to  repeat  digits  is  the  per  cent,  that  the.  number  of  points 
scored  is  of  the  number  of  points  possible  (i.e.  6  times  the  num- 
ber of  subjects  in  the  group). 

The  number  of  subjects  in  each  grade  (boys  and  girls  shown 
separately)  the  average  age  of  the  subjects  in  each  grade,  to- 
gether with  the  mean  variation  from  the  average  are  shown  in 
Table  3. 

TABLE  3 

Number  of  Boys  and  Girls  in  Each  Grade,  and  the  Average  Age  of  All 

Subjects  in  Each  Grade. 

Number        Number  Total  No.       Average  Mean 

Grade              of  Boys        of  Girls  of  Subjects          Age  Variation 

Kindergarten 20                   12  32             5.64  years  0.46  years 

Grade  1 27                  24  51              705    "  0.50    " 

Grade  II 16                   24  40             8.16    "  0.65    " 

Grade  III 21                   24  45             9-31     "  0.75    " 

Grade  IV 20                   15  35            10.46    " '  0.91     " 

Grade  V 24                  25  49            11.71     "  0.99    " 

Grade  VI 33                   16  49            12.81     "  1.06    " 

The  above  table  shows  an  increase  of  a  year  or  more  (actually 
from  1. 10  years  to  1.41  years)  in  the  average  age  of  the  subjects 
in  each  grade.  From  this  it  is  reasonable  to  expect  that  there  is 
a  general  growth  in  intelligence  correlating  with  this  increase  in 
age,  or,  in  other  words,  to  expect  a  correlation  between  the  re- 
sults of  the  individual  tests  and  the  grade  in  which  the  per- 
formance occurred.  If  the  correlation  is  too  high,  it  will  in- 
dicate a  dependence  of  that  particular  test  on  the  subject  matter  of 
the  grade.  In  Table  4  are  shown  the  percentages  that  the  sub- 
jects in  each  grade  passed  each  test.  The  notes  referred  to  in 
the  margin  contain  the  proportions  passed  for  all  other  subjects 
for  whom  the  percentages  are  not  given,  the  percentages  being 
given  only  for  those  groups  to  whom  the  tests  were  given  from 
75%  to  100%  of  the  possible  number  of  tirries. 

A  study  of  Table  4  shows  that  the  tests  in  general  correlate 
with  grade.  The  combined  score  of  the  test  of  repeating  digits, 
for  example,  shows  a  growth  from  6%  to  78%,  more  rapid 
in  the  first  three  grades  than  in  the  last  four.     The  tests  vary  in 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  45 

TABLE  4 

Percentage  that  Subjects  in  Each  Grade  Passed  Each  Test.    301  Subjects. 

Grades 

Test                                      K  I         II  III      IV        V       VI 

VII-i,  13  pennies   72  96      100  Note    I 

VII-2,  Pictures  69  96        94  Note    2 

VII-4,  Diamond  46  75        88  Note    3 

VII-5,  Colors  72  90       97  Note    i 

VIII-2,  20  to  0   9        53  80                                    Note    4 

VIII-4,  Stamps    13        50  78                                    Note    5 

All  digits,   (combined) 6  21        42  51         55        78        75 

VIII-3,  Days  of  week 16  45        90  100                                     Note    6 

IX-3,  Date   5        35  96      100                          Note    7 

IX-4,  Months  28  84        90                          Note    8 

X-I,  Money  20  2,(>        57        82               Note    9 

X-2,  Designs  21        37        42        66    Note  10 

X-s,  Sentence   (2  ideas)..  67        89        88        98    Note  11 

XI-2,  Sentence  (i  idea)...-  22        46        51        74    Note  12 

XI-3,  60  words   63        63        87    Note  13 

XI-4,  Rhymes   67        63        76    Note  14 

Note     I.  Counting  13  pennies  and  naming  colors  given  20  times  above  II. 

Not  failed. 
Note    2.  Describing  pictures  given  21  times  above  II.     Not  failed. 
Note    3.  Copying  diamond  given  25  times  above  II.     Not  failed. 
Note    4.  Counting  from  20  to  0  given  18  times  in  K.     Not  passed.     Given 

31  times  above  III.     Failed  once. 
Note    5.  Counting  stamps  given  15  times  in  K.     Not  passed.    Given  35  times 

above  III.    Failed  3  times. 
Note    6.  Naming  days  of  week.    Given  32  times  above  III.    Not  failed. 
Note    7.  Giving  day  and  date  given  5  times  in  K.     Not  passed.     Given  56 

times  above  IV.     Not  failed. 
Note    8.  Naming  months.     Given  26  times  below  II.     Passed  twice.     Given 

44  times  above  IV.     Failed  twice. 
Note    9.  Naming  money.    Given  26  times  below  II.    Passed  3  times.    Given 

28  times  in  VI.     Failed  twice. 
Note  10.  Copying  designs  given  33  times  below  III.     Passed  5  times. 
Note  II.  Sentence  (2  ideas)  given  32  times  below  III.    Passed  12  times. 
Note  12.  Sentence  (i  idea)  given  32  times  below  III.     Passed  4  times. 
Note  13.  Giving  60  words  given  53  times  below  IV.    Passed  19  times. 
Note  14.  Giving  rhymes  given  42  times  below  IV.     Passed  26  times. 

the  number  of  grades  taken  to  reach  their  maximum.  The  test 
of  naming  the  day  and  date,  for  example,  is  failed  by  all  subjects 
in  the  kindergarten,  95%  of  Grade  I  and  65%  of  Grade  II,  while 
only  4%  of  the  subjects  in  Grade  III  and  none  of  those  in  the 


46  CARL  C.  BRIGHAM 

higher  grades  fail  it.  A  sudden  increase  occurs  between  Grades 
II  and  III  showing  possibly  the  influence  Of  grade  training.  The 
tests  vary  considerably  in  the  degree  of  their  correlation.  An 
easily  obtained  measure  of  the  degree  of  correlation  is  that  of 
comparing  the  magnitude  of  the  increases  from  grade  to  grade. 
For  example,  there  is  an  increase  of  6i%  (96% — 35%)  from 
Grade  II  to  Grade  III  in  the  ability  to  pass  the  test  of  giving  the 
day  and  date,  and  an  increase  of  16%  (36 — 20%)  between  the 
same  grades  in  the  test  of  naming  the  pieces  of  money.  The 
former  test  correlates  higher  with  the  influence  of  grade  in  this 
particular  case  than  the  latter. 

In  this  manner  the  percentage  difference  between  the  per- 
formance of  the  subjects  in  each  grade  and  that  of  the  subjects 
in  the  preceding  grade  was  obtained.  All  the  increases  or  de- 
creases in  ability  from  one  grade  to  another  were  thus  obtained, 
these  values  serving  as  measures  of  the  amount  of  correlation 
between  the  tests  and  the  grades.  42  differences  between  the 
performance  of  the  subjects  in  any  grade  and  those  of  the  next 
succeeding  grade  were  thus  obtained.  In  4  cases  there  were 
actual  decreases  of  i,  2,  3  and  4%  which  were  not  significant.  The 
difference  ranged  from  — 4%  to  +61%,  the  median  being 
+  19.5%  (Q=i6.25%).  Some  of  the  differences  between  the 
grades  might  be  due  to  the  chance  superiority  of  a  particular 
grade.  To  overcome  this  chance  variation,  and  to  furnish  an- 
other index  of  the  growth  of  the  various  abilities,  the  differences 
were  calculated  by  steps  of  two  grades,  i.e.,  sulbtracting  the  per- 
formance of  the  kindergarten  from  the  second  grade,  the  first 
from  the  third,  etc.  In  this  way,  26  differences  were  obtained 
varying  from  +9%  to +91%,  the  median  being  -{-29% 
(Q=i8%). 

Some  of  the  differences  noted  are  undoubtedly  high  enough  to 
warrant  the  assumption  of  the  effect  of  grade  training  on  the 
tests.  Just  what  tests  show  this  effect  is  probably  a  matter  of  opin- 
ion. Allowance  must  be  made  for  the  growth  of  an  ability 
independent  of  training.  25%  of  the  highest  increases  from 
one  grade  to  another  were  selected  as  being  worthy  of  special 
consideration  at  least.     A  larger  increase  must  be  allowed  be- 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  47 

tween  two  grades.  Those  differences  were  considered  worthy 
of  special  consideration  that  exceeded  twice  the  value  of  the 
median  of  the  one-grade  differences  or  39%.  This  manner  of 
selecting  the  largest  differences  is  quite  arbitrary,  but  is  justified 
by  the  outcome,  for  the  tests  that  show  the  most  significant  in- 
-  reases  according  to  this  method  show  those  increases  in  more 
than  one  step,  so  that  the  evidence  is  concentrated  against  a  very 
few  tests.  In  this  way  the  significant  values  outweigh  the  less 
significant  values  and  fair  allowance  is  made  for  growth  from 
one  grade  to  another. 

The  following  list  includes  the  tests  showing  the  greatest  in- 
creases by  one-grade  and  two-grade  steps,  together  with  the 
magnitude  of  the  increases  and  the  grades  between  which  they 
occur. 

One-grade  steps.  Two-grade   steps. 

25%  of  largest  Increases  greater 

increases.  than  39%. 

-1-61%  Date,  II  to  III  -f9i%  Date,  I  to  III 

+56%  Months,  II  to  III  +74%  Days,  K  to  II 

+71%  20  to  o,  I  to  III 

-f-45%  Days,  I  to  II 

+44%  20  to  0,  I  to  II  -1-65%  Stamps,  I  to  III 

-1-65%  Date,  II  to  IV 

+37%  Stamps,  I  to  II  -f  62%  Months,  II  to  IV 


-f-30%  Date,  I  to  II 


-1-55%  Days,  I  to  III 


-|-29%  Diamond,  K  to  I 

+29%  Days,  K  to  I  -|-46%  Money,  III  to  IV 

-f-28%  Stamps,  II  to  III  -[-42%  Diamond,  K  to  II 

+27%  20  to  o,  II  to  III 

+27%  Pictures,  K  to  I 

The  above  lists  of  increases  are  confined  to  but  8  tests.  In 
all,  there  were  16  tests  studied.  According  to  the  method  of 
selecting  the  significant  increases,  20  such  values  actually  ap- 
peared. In  this  manner  the  evidence  combines  against  a  very 
few  tests.  Some  tests  appear  in  both  lists  and  more  than  once 
in  the  same  list.  The  most  striking  growth  with  grade  is  shown 
in  the  tests  of  giving  the  day  and  date,  naming  the  months,  nam- 


48  CARL  C.  BRIGHAM 

ing  the  days  of  the  week,  counting  from  20  to  o  and  counting 
stamps.  The  tests  of  copying  the  diamond,  describing  pictures 
and  naming  money  may  or  may  not  show  this  influence.  The 
evidence  is  strongest  in  the  case  of  the  diamond  test  since  that 
appears  in  both  lists. 

The  foregoing  method  of  selecting  those  tests  which  correlate 
with  grade  to  such  an  extent  as  to  indicate  the  influence  of  grade 
training  is  not  conclusive,  owing  to  the  fact  that  there  is  also 
an  increase  in  age  from  grade  to  grade.  If  a  test  showed  a 
very  rapid  growth  with  age,  and  those  ages  fell  for  the  most  part 
in  certain  grades,  then  those  grades  would  show  an  increase  which 
might  be  wrongly  assumed  to  be  due  to  training.  The  tests  of 
counting  from  20  to  o  is  a  case  in  point.  Yerkes  (82)  in  Table 
32,  page  125,  gives  the  percentage  values  for  each  test  in  the 
Point  Scale,  for  English  speaking  boys  and  girls  of  each  age. 
The  test,  of  the  twenty  one  tests  included,  that  shows  the  most 
marked  increase  with  age  is  that  of  counting  backward,  the 
values  being  as  follows, —  age  4=0%;  age  5^3.5%;  age 
6=23.7%;  age  7=45.7%;  age  8=72.2%;  age  9=96%;  the 
values  for  ages  above  9  being  97%  or  higher. 

The  age  in  grade  distribution  of  the  301  subjects  in  this  in- 
vestigation is  given  in  Table  5. 

TABLE  5 
Distribution  of  Subjects  in  Each  Grade  according  to  Chronological  Age. 

Grades 


Age 

K 

I 

II 

III 

IV 

V 

VI 

Total 

4 

4 

4 

5 

17 

^7 

6 

II 

28 

2 

41 

7 

18 

17 

2 

I 

38 

8 

4 

15 

18 

I 

38 

9 

5 

13 

II 

29 

10 

I 

10 

14 

18 

I 

44 

11 

I 

2 

3 

\6 

16 

38 

12 

5 

8 

II 

24 

13 

'- 

4 

12 

16 

14 

2 

5 

7 

15 

I 

3 

4 

16 

I 

I 

Total 

32 

51 

40 

45 

35 

49 

49 

301 

VARIABLE  FACTORS  IN  THE  BINET  TESTS  49 

The  rapid  growth  of  the  abihty  in  counting  from  20  to  o, 
according  to  the  method  of  comparing  the  subjects  in  each  grade, 
was  from  9%  in  Grade  I  to  80%  in  Grade  III.  From  Table  5 
it  may  be  seen  that  practically  all,  (89%),  of  the  chronolog- 
ical ages  in  Grades  I,  II  and  III  were  distributed  in  the  ages 
6,  7,  8  and  9,  a  chronological  range  coinciding  with  that  in  which 
Yerkes'  results  show  the  ability  to  develop.  The  growth  of 
this  ability  might  be  due  then  either  to  age  or  to  grade.  For 
this  reason,  to  arrive  at  any  final  conclusion,  it  is  necessary  to 
compare  the  subjects  of  the  same  age  but  in  different  grades. 
The  treatment  of  the  Princeton  results  according  to  this  method 
follows,  but  the  analysis  of  the  data  in  this  manner  can  have 
no  great  reliability  owing  to  the  small  number  of  subjects  in  each 
group.  The  number  of  subjects  in  each  group,  (boys  and  girls 
shown  separately),  the  average  age  and  mean  variation  from  this 
average  are  shown  in  Table  6. 

TABLE  6 

Number  of  Boys  and  Girls  of  Similar  Ages  in  Different  Grades,  and  the 

Average  Age  of  the  Subjects  of  Similar  Ages  in  Each  Grade. 

Number    Number      Total  no.     Average  Mean 

Grade  Age         of  Boys      of  Girls    of  Subjects      Age  Variation 

Kindergarten.     5  11  6  17  5.48  0.20 

Kindergarten.     6  8  3  11  6^  0.21 

Grade  I  6  14  14  28  6.59  0.17 

Grade  I  7  9  9  18  7.36  0.22 

Grade  II   7  7  10  17  7.56  0.24 

Grade  II  8  6  9  15  8.39  0.24 

Grade  III   ...     8  8  10  18  8.60  0.22 

Grade  III  ...     9  5  8  13  9.43  0.16 

Grade  IV  ....    9  5  6  11  9.65  0.13 

Grade  IV  10  10  4  14  10.39  0.30 

Grade  V  10  7  11  18  10.54  0.25 

Grade  V  11  10  6  16  11.54  0.22 

Grade  VI  ...  11  10  6  16  11.53  0.26 

Grade  VI  12  6  5  11  12.52  0.14 

All  chronological  ages  were  computed  in  tenths  of  a  year,  so 
that  a  variation  in  age  from  o.i  yr.  to  0.9  yr.  is  possible  within 


so 


CARL  C.  BRIGHAM 


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VARIABLE  FACTORS  IN  THE  BINET  TESTS  Si 

Note    I.  Tests  of  counting  13  pennies,  describing  pictures  and  naming  colors 

each  given  12  times  above  II-8.     No  failures. 
Note    2.  Copying  diamond  given  15  times  above  II-8.    No  failures. 
Note    3.  Counting  from  20  to  o  given  16  times  below  1-6.    Not  passed.    Given 

31  times  above  III-8.    Failed  4  times. 
Note    4.  Counting  stamps  given  14  times  below  1-6.     Not  passed.    Given  32 

times  above  III-8.    Failed  4  times. 
Note    5.  Giving  days  of  week  given  ^2  times  above  III-8.    No  failures. 
Note    6.  Giving  date  given  39  times  below  II-7.     Passed  twice.     Given  36 

times  above  IV-io.    No  failures. 
Note    7.  Naming  months  given  24  times  below  II-7.     Passed  twice.     Given 

37  times  above  IV-9.    Failed  4  times. 
Note    8.  Naming  pieces  of  money  given  35  times  below  II-8.    Passed  4  times. 

Given  14  times  above  V-ii.    Failed  twice. 
Note    9.  Copying  designs  given  26  times  below  III-8.    Passed  5  times.    Given 

15  times  above  V-ii.    Failed  6  times. 
Note  ID.  Three  words  in  sentence,  2  ideas,  given  24  times  below  III-8.  Passed 

9  times. 
Note  II.  Sentence,  i  idea,  given  same  as  2.    Passed  3  times. 
Note  12.  60  words  in  3  minutes  given  41  times   below  IV-9.    Passed  10  times. 
Note  13.  Giving  rhymes  given  37  times  below  IV-io.     Passed  25  times. 

each  age  group.  That  the  subjects  of  the  "same"  age  but  in 
different  grades  are  not  exactly  the  same  is  shown  in  Table  6. 
The  subjects  of  each  age  in  the  higher  grades  average  from 
o.oi  yr.  to  0.33  yr.  different,  with  an  average  superiority  of 
0.19  yr.  This  difference,  however,  is  about  one  fourth  that 
between  the  subjects  or  different  ages  in  the  same  grades,  and 
may  be  called  the  same  for  practical  purposes.  For  convenience, 
the  groups  will  be  referred  to  as  K-5,  II-7  etc.,  the  first  member 
referring  to  the  grade,  the  second  to  the  age.  K-5  would  mean 
the  group  of  5  year  children  in  the  kindergarten,  II-7,  the  7  year 
subjects  in  Gr^de  II,  etc.  The  actual  per  cent,  that  the  subjects  in 
each  group  passed  each  test  was  calculated  and  is  shown  in  Table 
7.  Unless  otherwise  noted,  the  percentages  are  based  on  tests 
given  75%  to  100%  of  the  possible  number  of  times. 

Some  of  the  groups  from  which  results  were  obtained  are  too 
small  to  have  great  reliability,  but  the  method  is  at  least  sug- 
gestive. The  results  of  14  groups  are  given.  It  is  possible  then 
to  compare  the  results  of  subjects  of  6  ages,  (6,  7,  8,  9,  10 
and  11),  that  are  in  different  grades,  and  also  to  compare  sub- 


52  CARL  C.  BRIGHAM 

jects  in  all  seven  grades  that  are  of  different  ages,  and  in  this 
way  to  determine  whether  the  dominating  factor  in  the  growth 
of  any  ability  is  that  of  grade  or  age.  The  reliability  of  the 
method  rests  only  on  its  connection  with  that  of  the  first  method 
employed. 

In  answer  to  the  question  of  whether  the  growth  of  ability  in 
the  test  of  counting  from  20  to  o  is  due  to  age  or  grade,  a  ques- 
tion which  was  unanswered  by  the  first  method,  we  may  turn  to 
the  results  shown  in  Table  7  in  which  the  subjects  of  each  age  in 
each  grade  are  shown.  The  test  of  counting  from  20  to  o  was  not 
passed  by  any  of  the  5  and  6  year  subjects  in  the  kindergarten. 
Comparing  first  the  subjects  of  different  ages  in  the  same  grade, 
the  7  year  subjects  in  Grade  i  are  16%  lower  than  the  6  year 
subjects  in  that  grade,  and  the  8  year  subjects  in  Grade  II  are 
20%  lower  than  the  7  year  subjects  in  the  same  grade,  the  older 
subjects  making  a  lower  record  in  each  case.  Comparing  the 
performance  of  the  subjects  of  the  same  age  but  in  different 
grades,  the  7  year  subjects  in  Grade  II  are  63%  ahead  of  the 
subjects  of  the  same  age  in  Grade  I,  while  the  8  year  subjects 
are  40%  ^  ahead  of  the  subjects  of  the  same  age  in  Grade  II. 
Allowing  for  the  retrogression  of  the  older  subjects  in  each 
group,  i.e.  assuming  that  they  should  have  done  equally  as  well 
as  the  younger  subjects  in  the  same  grade,  the  groups  in  Grades 
II  and  III  are  still  47%  and  20%  ahead  of  the  subjects  in  the 
grades  lower.  The  growth  of  ability  in  this  test  would  therefore 
appear  to  be  due  to  grade  training. 

A  rapid  growth  of  ability  in  the  test  of  counting  stamps  oc- 
curred between  Grades  I  and  III  (37%  1-11+28%  11-111=65% 
I-III),  according  to  the  first  method,  so  that  the  same  question 
arises  as  in  the  test  of  counting  from  20  to  o.  The  test  was  not 
passed  below  group  1-6.     No  growth  with  age  is  shown  between 

iThis  test  was  given  to  but  66%  of  the  subjects  in  III-8,  the  experimenters 
assuming  that  the  other  34%  would  pass.  The  score  given,  85%,  therefore 
represents  the  ability  of  the  lowest  selection  of  III-8  subjects,  or  the  most 
conservative  estimate  of  the  ability  of  the  whole  group.  The  same  applies 
to  the  other  tests  in  III-8  given  66%  and  72%  of  the  time.  In  this  way  the 
hypothesis  that  the  tests  are  not  influenced  by  grade  training  is  given  the 
benefit  of  the  doubt. 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  53 

1-6  and  I-7,  but  a  growth  of  31%  appears  between  II-7  and  II-8. 
A  growth  with  grade  of  17%  is  shown  from  I-7  to  II-7  and  of 
25%  from  II-8  to  III-8.  This  test  shows  therefore  the  operation 
of  the  two  factors  of  age  and  grade  training. 

The  improvement  in  abiHty  in  the  tests  of  counting  13  pen- 
nies, describing  pictures  and  naming  colors,  that  was  indicated 
between  the  kindergarten  and  Grade  I  by  the  first  method,  would 
refer  to  age  rather  than  grade,  for  a  greater  increase  in  each 
test  is  indicated  between  K-5  and  K-6  than  between  K-6 
and  1-6.  Above  1-6  these  abilities  are  completely  developed. 
It  could  be  maintained  that  these  tests  are  so  completely 
within  the  ability  of  the  groups  that  the  effect  of  train- 
ing would  not  be  indicated.  The  test  that  is  best  adapted 
to  show  the  influence  of  any  factor  on  a  group  is  one  that 
is  well  within  the  ability  of  the  group — the  influence  of  the  factor 
will  be  obscured  if  the  measure  is  either  too  easy  or  too  difficult. 
The  test  of  copying  the  diamond  is  a  case  in  point  and  one  well 
worth  study,  for  it  has  been  attributed  to  the  effect  of  training 
by  various  authors.  All  the  reproductions  of  the  diamond  had 
been  scored  according  to  the  arbitrary  system  outlined  in  the 
previous  discussion  of  the  personal  equation.  A  control  on  the 
factor  of  difficulty  was  obtained  by  raising  or  lowering  the  pass- 
ing mark  in  this  test.  The  percentage  passed  was  calculated  for 
each  group  for  each  of  the  5  possible  passing  marks.  The  re- 
lations indicated  in  Table  7,  where  the  passing  mark  is  Group  IV, 
were  not  changed  by  this  process  of  raising  or  lowering  the  pass- 
ing mark.  In  all  cases  the  influence  of  age  was  shown  between 
groups  1-6  and  I-7,  and  the  influence  of  grade  shown  between 
groups  K-6  and  1-6.  The  test  was  given  to  but  59%  of  the  K-5 
group,  the  experimenter  assuming  that  the  other  41%  would 
fail,  so  that  the  percentages  calculated  represent  the  performance 
of  the  best  selection  of  K-5  subjects,  or,  in  other  words,  the 
benefit  of  the  doubt  is  given  to  the  hypothesis  that  the  test  is 
influenced  by  grade  training.  If  the  other  members  of  K-5  had 
failed  according  to  the  experimenter's  assumption,  (and  this 
assumption  was  quite  justified  for  some  had  failed  to  draw  the 
square),  29%  of  the  group  would  have  passed  instead  of  50%. 


54  CARL  C.  B  RICH  AM 

The  influence  of  age  indicated  in  this  test  is  as  great  if  not  greater 
than  that  due  to  training. 

The  test  of  repeating  digits,  scored  by  the  weighting  system 
previously  described,  exhibits  a  slow  but  uniform  progress 
throughout,  the  older  subjects  in  each  group  making  records  that 
are  about  the  same  or  slig'htly  lower  than  those  of  the  younger 
subjects  in  the  same  grade,  an  increase  showing  fairly  regularly 
from  grade  to  grade.  The  most  marked  increase  in  this  ability 
appears  between  K-6  and  1-6,  and  between  I-7  and  II-7,  possibly 
indicating  that  the  lack  of  familiarity  with  the  use  of  digits  in 
the  lowest  grades  interferes  with  this  test  as  a  measure  of 
auditory  memory. 

The  test  of  naming  the  days  of  the  week  shows  the  most 
marked  improvement  with  age  (40%)  from  K-5  to  K-6,  prac- 
tically no  improvement  (10%),  from  K-6  to  1-6,  no  improvement 
from  1-6  to  I-7,  a  very  marked  increase  with  grade  from  I-7  to 
II-7,  a  drop  from  II-7  to  II-8,  group  III-8  marking  the  complete 
development  of  the  ability.  The  test  would  appear  to  be  due  to 
the  combined  effect  of  age  and  grade.  The  tests  of  giving  the 
day  and  date  and  naming  the  months  are  passed  only  twice  in 
the  kindergarten  and  first  grade,  by  about  a  quarter  of  the  sub- 
jects in  II-7  and  II-8  without  age  increase,  while  the  subjects  in 
III-8  shows  a  most  marked  increase  due  to  grade.  Above  III-8 
these  tests  are  seldom  failed.  The  test  of  naming  the  pieces  of 
money  shows  a  slow  growth  from  8  to  11,  the  largest  increases 
appearing  from  III-9  to  IV-9  and  from  IV- 10  to  V-io,  improve- 
ment with  grade  in  each  case.  Copying  the  designs  from  memory 
shows  a  growth  of  26%  from  8  to  11,  the  development  occurring 
in  two  age  steps,  from  IV-9  to  IV- 10  and  from  V-io  to  V-ii. 

The  growth  with  age  cannot  be  determined  in  the  tests  of  con- 
structing sentences  from  three  given  words,  because  they  were 
given  to  too  few  cases  below  the  third  grade.  The  results  do  not 
show  whether  III-8  is  exceptionally  high  or  III-9  exceptionally 
low.  Both  tests  show  decreases  in  ability  from  III-8  to  III-9  and 
from  V-IO  to  V-ii.  The  ability  in  the  easier  test  is  well  within 
the  range  of  the  third  and  higher  grades,  showing,  therefore,  no 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  55 

improvement.  The  improvement  in  the  second  test  develops 
from  33%  to  80%  in  three  steps,  correlating  with  Grades  IV,  V 
and  VI  in  each  case.  The  most  vital  question,  that  of  determin- 
ing whether  or  not  the  language  training  in  the  third  grade  helps 
to  make  the  construction  of  a  sentence  possible,  cannot  be  deter- 
mined owing  to  the  lack  of  material  in  the  second  grade.  The 
experimenters'  assumptions  in  not  trying  the  test  would  indicate 
this  fact,  but  this  is  not  experiment.  The  same  lack  of  material 
makes  conclusions  in  regard  to  the  rhyming  test  impossible.  The 
performance  of  IV-io  is  exceeded  only  by  VI-ii.  The  test  of 
naming  60  words  in  three  minutes  shows  two  decided  increases 
with  age  and  one  decided  drop  with  grade. 

The  foregoing  analysis  is  based  on  a  number  of  subjects  in 
each  group  too  small  to  have  any  great  significance.  The  general 
fact  of  the  correlation  of  the  tests  with  grade  remains,  and  con- 
clusions concerning  what  tests  correlate  too  highly  with  training 
can  be  answered  only  by  considering  both  methods  of  study,  and 
by  considering  only  the  largest  deviations.  The  two  most  strik- 
ing instances  are  found  in  the  tests  of  naming  the  months  and 
giving  the  date.  These  tests  undoubtedly  relate  almost  entirely 
to  training.  Less  striking  but  equally  definite  is  the  relation  of 
the  test  of  counting  from  20  to  o  to  training.  The  tests  of 
naming  the  days  of  the  week  and  counting  stamps  show  the  in- 
fluence of  age  to  an  extent  almost  as  marked  as  that  of  grade,  so 
that  while  the  development  in  these  tests  is  rapid,  the  grade  factor 
probably  exerts  only  part  of  the  influence.  Conclusions  concern- 
ing the  other  tests  are  largely  a  matter  of  opinion,  and  the  opinion 
of  the  writer  has  been  indicated  in  the  detailed  discussion. 

A  study  of  the  tests  in  relation  to  grade  by  the  first  method 
employed  may  be  made  from  Schmitt's  results.  The  author 
gives,  in  Table  I,  II,  III,  IV,  V,  VI  and  VII  on  pages  70,  71,  73, 
74,  75,  76  and  yy  of  her  monograph,  the  results  of  each  subject 
in  each  grade  on  each  test.  From  these  tables  the  present  writer 
has  calculated  the  percentage  passed  in  each  test.  A  study  of 
this  sort  rests  for  its  reliability  on  the  accuracy  of  the  published 
tables,  and  the  facts  indicated  by  the  tables  do  not  always  coincide 


S6  CARL  C.  BRIG  HAM 

with  Schmitt's  discussion.^  The  writer  has  followed  the  tables 
rather  than  the  discussion  in  calculating  the  results.  In  the  VIII-2 
test  where  an  alternative  rank  is  given  for  counting  from  10  to  o 
instead  of  20  to  o,  the  writer  has  considered  success  in  counting 
from  10  to  o  as  a  failure  in  counting  from  20  to  o.  In  the  line 
suggestion  test  Schmitt  recognizes  two  types  of  failure,  the 
typical  failure  according  to  Binet  of  accepting  the  suggestion  of 
the  first  three  lines,  and  the  failure  due  to  the  fact  that  the  subject 
actually  judges  the  lines  unequal  after  studying  them.  The  sec- 
ond type  of  response  Schmitt  marks  as  passed,  using  a  special 
symbol.  The  writer  has  calculated  these  percentages  separately, 
entering  the  first  or  Binet  type  of  response  under  "Line  sugges- 
tion A"  in  the  table,  and  the  second  type  under  "B."  The  V  year 
and  Adult  tests  were  omitted.  All  of  the  other  tests  were  in- 
cluded that  had  been  given  over  70%  of  the  possible  number  of 
times.  Unless  otherwise  noted,  each  test  was  given  100%  of 
the  possible  number  of  times.  Table  8  shows  the  per  cent,  that 
Schmitt's  subjects  in  each  grade  passed  each  test  in  Binet's  191 1 
scale  (Town's  translation  with  modifications).  The  table  is 
given  with  the  reservation  that  the  tables  from  which  the  per- 
centages were  calculated  might  contain  misprints,  and  that  the 
writer's  interpretation  of  the  tables  might  be  at  fault. 

Inasmuch  as  there  are  many  differences  in  procedure  in  giving 
the  tests,  and  in  the  character  of  the  schools  tested,  the  results  of 
the  two  investigations  are  not  comparable  in  respect  to  the  per- 
centage passed  in  one  grade  in  one  study  with  those  in  the  same 
grade  in  the  other  study.     The  method  used  in  determining  the 

2  In  the  discussion  (page  69)  Schmitt  gives  15  subjects  in  the  kindergarten 
failing  test  VII-4.  Table  I  shows  13.  On  the  same  page  she  gives  24  sub- 
jects failing  VIII-4.  Table  I  shows  22  failing.  In  discussing  the  results 
of  Grade  I  (page  72)  Schmitt  states  that  there  is  "more  than  50%  of  failure 
with  the  discrimination  of  weight",  while  Table  II  shows  35%  failure.  Again, 
the  tests  referred  to  specific  school  instruction  by  Schmitt  are  VII-4,  VIII-4, 
and  IX  I,  2,  3  and  4.  On  page  72,  in  discussing  the  results  of  Grade  I,  she 
says  "the  tests  below  ten  years  which  depend  upon  specific  instruction  are 
usually  not  passed  except  the  VII-4  test.  The  percentages  passed  are  as 
follows:  VII-4  =  85%;  VIII-4  =  45%;  IX-i  =  35%;  IX-2  =  75%; 
IX-3=90% ;  IX-4=30%.  "Usually  not  passed"  includes,  therefore,  tests 
passed  75%  and  90%  of  the  time. 


VARIABLE  FACTORS  IN  THE  BINET  TESTS 


57 


TABLE  8 


Number  of  subjects 
VI-i,  Distinguishing  morning,  afternoon 

2.  Defining  in  terms  of  use 

3,  Copying  diamond 
Counting  13  pennies 
Choosing  prettier  of  faces 
Showing  right  hand 
Describing  pictures 
Executing  3  commissions 
Counting  stamps 
Naming  colors 

Comparing  remembered  objects 
Counting  backwards  from  20  to  0 
Indicating  omissions   in  pictures 
Giving  day  and  date 
Repeating  5  digits 
Making  change 

Defining  in  terms  superior  to  use 
Naming  pieces  of  money 
Naming  the  months 
Comprehending  easy  questions 
Arranging  5  weights 
Copying  designs 
Detecting  absurdities 
Comprehending  difficult  questions 
Constructing  sentence.     Two  ideas 
Resisting  suggestion,  A.    (Binet  scoring) 
B.  Judgment  error  counted  plus 
Constructing  sentence.     One  idea 
Giving  60  words  in  three  minutes 
Defining  abstract  terms 
Reconstructing  dissected  sentences 
Repeating  7  digits 
Rhyming  words  with  "obey" 
Repeating  a  sentence  of  26  syllables 
Interpreting  pictures 
Solving  problems  from  various  facts 


4: 

5 
VII-i 

2, 
3 

4: 

5. 
VIII-i 
2, 
3 
4 
5 
IX-i 
2, 
3 

4: 

5 

X-i 

2 

3 

4: 

5 
XII-i 


2, 
3 

4: 

5 
XV-i 
2 
3 
4, 
5 


rade 

Passed 

Eacl 

i  Test. 

150 

Subjects. 

Grades 

K 

I 

II 

III 

IV 

V 

VI 

25 

20 

17 

21 

22 

22 

23 

96 

100* 

92 

94* 

76 

94* 

92 

100* 

92 

100* 

92 

80 

100 

72 

65 

81 

92 

95 

100 

48 

85 

100 

96 

100 

100 

92 

100 

100 

100 

100 

40 

85 

94 

95 

100 

100 

95 

94 

100 

100 

12 

45 

94 

100 

100 

64 

85 

94 

100 

100 

6* 

35 

71 

95 

86 

100 

39* 

75 

65 

100 

95 

100 

28* 

90 

94 

100 

100 

100 

6* 

30 

71 

95 

95 

95 

61* 

100 

100 

95 

100 

100 

65 

41 

57 

50 

64 

ID 

35 

57 

45 

32 

60 

88 

100 

100 

100 

85 

100 

100 

100 

100 

65 

76 

100 

100 

100 

ng) 

64* 

76 

52 
100 

41 
86 

14* 

100* 

100 

57* 

71 

95 

95 

100* 

100 

43* 

82 

62 

100 

95* 

96 

7* 

29 

52 

7Z 

95* 

100 

0* 

6 

10 

23 

81* 
62* 
86* 
10* 
14* 
62* 

78 
78 
70 

17 
70 
70 

Note. — All  tests  except  those  marked  (*)  were  given  all  the  possible  number  of 
times.  The  VI  year  tests  were  given  90%  of  the  time  in  Grade  I,  the  IX  year  tests 
72%  of  the  time  in  the  kindergarten,  the  XII  year  tests  70%  of  the  time  in  Grade  I, 
and  the  XII  and  XV  year  tests  95%  of  the  time  in  Grade  V. 


58  CARL  C.  BRIGHAM 

correlation  of  the  tests  with  grade  is  the  same  as  that  used  in 
the  first  method  of  treating  the  Princeton  data,  that  of  comparing 
the  differences  between  grades  by  one-grade  and  two-grade  steps, 
of  selecting  an  arbitrary  standard  for  detectjing  exceptional 
growth,  and  of  comparing  the  resulting  lists.  The  differences 
between  the  performance  of  each  grade  and  the  next  succeeding 
grade  were  calculated.  These  differences,  lOO  in  number,  ranged 
from  — 24%  to  +62%,  the  median  being  +5%  (Q=rio.75%). 
The  run  of  differences  differs  from  that  found  in  the  Princeton 
study  in  two  respects,  in  having  a  lower  median  and  variability, 
and  in  containing  more  minus  deviations.  The  lower  median  and 
variability  is  due  to  the  fact  that  the  tests  were  given  over  a 
wider  range,  the  Princeton  tests  being  given  only  on  the  "up 
slope"  of  the  growth  curve,  or  not  being  given  when  the  tests 
were  any  distance  above  or  below  the  probable  range  of  ability  of 
the  group.  The  Princeton  results  showed  only  4  minus  deviations 
of  4,  3,  2,  and  1%  respectively,  while  Schmitt's  results  show  15 
such  deviations,  6  of  them  being  10%  or  over.  These  deviations 
are  probably  due  to  the  smaller  number  of  subjects,  and  if  due 
to  chance,  should  be  counteracted  by  the  precautionary  measure 
of  combining  the  indices  of  correlation  into  two-grade  steps.  71 
two-grade  differences  were  obtained  ranging  from  —  25%  to 
+  82%,  the  median  being  +10%  (Qz=zi6.5%).  4  meas- 
ures were  still  in  the  minus  direction,  one  of  these,' — 25% 
(Design  III  to  V)  is  probably  significant,  the  other  values 
of  — 6%,  — 5%  and  — 4%  having  no  significance.  Inasmuch 
as  the  variability  of  the  series  is  lower,  those  differences 
were  considered  to  be  worthy  of  special  study  that  had  the 
value  of  2Q+M,  or  were  in  excess  of  the  interquartile  range 
plus  the  median.  The  lists  of  tests  that  appear  as  showing 
marked  growth  with  grade  according  to  the  two  methods  are 
as  follows : 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  59 

One  grade  differences  Two  grade  differences 

higher  than  2Q-J-M  higher  than  2Q4-M 

+62%,  IX-3,  Money,  K  to  I  +82%,  VIII-4,  Date,  K  to  II 

+58%,  XII-s,  Dissected,  IV  to  V  +7i%,  XII-s,  Dissected,  III  to  V 

+49%,  VIII-4,  Date,  I  to  II  +66%,  IX-3,  Money,  K  to  II 

4-457c,  VIII-2,  20  to  0,  K  to  I  +65%,  IX-4,  Months,  K  to  II 

+41%,  IX-4,  Months,  I  to  II  +65%,  IX-4,  Months,  I  to  III 

+65%,  IX-i,  Change,  K  to  II 


+60%,  IX-i,  Change,  I  to  III 


+39%>  IX-5,  Comprehension,  K  to  I 

+39%,  XII-3,  60  words,  I  to  II 

+38%,  XII-3,  6g  words.  III  to  IV  -f55%,  XII-5,  Dissected,  IV  to  VI 

+2>7%,  VII-4,  Stamps,  K  to  I  +55%,  VIII-4,  Date,  I  to  III 

+36%,  IX-2,  Definitions,  K  to  I  +54%,  VIII-2,  20  to  o,  K  to  II 

+36%,  IX-I,  Change,  I  to  II  +52%,  VII-4,  Stamps,  K  to  II 

+35%,  IX-2,  Definitions,  II  to  III 


+47%,  X-2,  Design,  I  to  III 
+45%,  XII-4,  Abstract  Def.,  I  to  III 
+29%,  IX-I,  Change,  K-I  +44%,  XII-4,  Abstract  Def.,  II  to  IV 


-\-32%,  VIII-4,  Date,  K  to  I 

+29%,  IX-I,  Change,  K-I 

+28%,  X-3,  Absurdities,  I  to  11  +437o,  XII-4,  Abstract  Def.,  Ill  to  V 


A  Study  of  the  above  lists  shows,  as  in  the  similar  study  of 
the  Princeton  data,  that  although  the  method  of  selecting  the 
exceptional  tests  is  an  arbitrary  one,  the  method  is  justified  in 
practice,  for  only  a  few  tests  (13)  appear  in  the  lists  as  signifi- 
cant. In  all,  there  were  34  tests'  studied,  and  30  differences  were 
considered  large  enough  to  be  significant.  These  30  differences 
were  confined  to  13  tests.  The  tests  of  naming  60  words  and 
defining  in  terms  of  use  drop  out  of  the  first  list  owing  to  the 
elimination  of  the  errors  of  negative  correlation.  The  design  test 
is  both  positive  and  negative,  the  ability  increasing  from  Grades 
I  to  III  and  decreasing  after  III.  The  test  of  defining  abstract 
terms  appears  according  to  the  second  rrtethod  because  the 
ability  increases  with  grade  from  7%   in  I  to  95%   in  V  by 

3  No  differences  were  calculated  from  the  line  suggestion  test  owing  to 
the  possibility  of  misinterpreting  the  symbols.  Schmitt  notes  the  difference 
in  the  character  of  the  responses  from  the  suggestion  error  to  the  judgment 
error  in  passing  from  Grade  II  to  III.  The  scoring  of  the  suggestion  error 
in  the  tables  shows  an  inverse  correlation  with  Grades  II,  III,  IV  and  V, 
and  a  sudden  change  again  from  14%  in  Grade  V  to  100%  in  Grade  VI,  so 
that  there  is  probably  a  mistake.  The  scoring  of  the  responses  to  this  test 
according  to  the  strict  Binet  ruling  would  make  the  "mental  ages"  lower, 
for  many  cases  would  then  have  basal  X. 


6o  CARL  C.  BRIGHAM 

increases  of  approximately  25%  in  each  grade.  No  conclusions 
may  be  drawn  concerning  the  easy  comprehension  test  and  the 
absurdities  test.  The  20  remaining  differences  are  confined  to  7 
tests,  those  of  naming  the  day  and  date,  naming  the  months, 
counting  from  20  to  o,  counting  stamps,  naming  money,  recon- 
structing dissected  sentences,  and  making  change.  The  first  four 
were  included  in  the  five  found  to  show  the  most  marked  influ- 
ence of  grade  in  the  Princeton  study.  The  test  of  naming  the 
pieces  of  money  did  not  show  a  marked  relation  to  grade  in  the 
latter  study,  but  this  difference  might  be  one  of  school  curriculum. 
The  test  of  naming  the  days  of  the  week  is  not  included  in  Binet's 
191 1  scale. 

In  the  Princeton  study  alternatives  were  used  in  the  making 
change  question  so  that  no  data  from  this  test  were  included  in 
the  quantitative  study.  These  data  show  the  ability  in  this  test 
developing  in  the  second  and  third  grades,  the  test  being  passed 
only  twice  in  the  kindergarten  and  first  grades,  and  generally 
passed  above  the  third.  The  data  in  the  test  of  reconstructing 
dissected  sentences  show  very  few  passing  the  test  below  grade 
V  with  approximately  three  fourths  passing  in  V  and  VI.  In  so 
far  as  the  Trenton  experimenting  was  applied  to  a  few  subjects 
in  the  regular  grades  below  the  seventh,  this  test  was  rarely 
passed  in  the  third  and  fourth  grade,  passed  about  5  %  in  V,  and 
almost  universally  passed  in  VI,  VII  and  VIII.  The  number  of 
subjects  in  each  grade  is  small  in  the  Trenton  experiment,  but 
each  test  was  separately  scored,  i.e.  each  part  of  the  dissected 
sentence  test,  each  part  of  the  absurdity  test  etc.  Each  of  the 
three  parts  of  the  dissected  sentence  test  showed  the  same  growth 
between  the  same  grades,  and  this  growth  was  more  marked 
than  that  in  any  other  test.  The  evidence  concerning  these  two 
tests,  therefore,  supports  the  evidence  from  Schmitt's  results. 

The  quantitative  analysis  of  the  Princeton  data  and  Schmitt's 
data  would  indicate  that  the  tests  of  counting  stamps,  counting 
from  20  to  o,  naming  the  days  of  the  week,  giving  the  day  and 
date,  naming  the  months,  naming  the  pieces  of  money,  making 
change  and  reconstructing  dissected  sentences  were  influenced  to 
a  considerable  extent  by  grade  training.     The  performance  in 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  6i 

certain  of  these  tests  (days,  date  and  months)  may  be  the  result 
of  specific  school  training  in  the  tests  themselves,  while  others 
(perhaps  the  tests  of  counting  stamps,  counting  from  20  to  o, 
and  reconstructino-  dissected  sentences)  may  involve  a  transfer 
effect  in  the  application  of  the  content  of  the  grade  in  a  new  way. 
The  fact  that  the  tests  correlate  very  highly  with  grade  training 
does  not  show  that  the  tests  are  worthless,  but  it  does  show  that 
they  should,  perhaps,  be  placed  in  another  scale,  or  should  at 
least  be  placed  on  a  different  footing  than  those  that  test  capacity 
irrespective  of  attainments. 

One  of  the  best  tests*  of  intelligence  is  the  determination  of 
what  an  individual  can  do  with  the  training  he  has  received,  but 
tests  of  this  sort  rest  on  the  assumption  that  the  individual's 
opportunities  have  been  determined.  The  importance  of  tests  of 
information  in  cases  of  alienation  presenting  a  picture  of  deteri- 
oration is  recognized.  The  important  change  to  be  made  is  not 
the  elimination  of  such  tests  from  intelligence  scales,  but  their 
standardization  on  a  different  basis.  The  diagnostic  value  of 
such  tests  rests  not  in  the  mechanical  memorizing  of  a  time 
series  such  as  that  of  the  months,  but  in  the  ability  to  apply 
such  a  series.  In  pointing  out  this  fact  Katzenellenbogen  (37) 
suggests  that  the  months  test  be  given  in  some  such  manner  as 
*Tf  somebody  asks  you  in  November  to  return  three  months  later, 
what  month  would  it  be?"  Decroly  and  Degand  also  suggest 
that  the  mechanical  tests  of  counting  and  naming  the  days  of  the 
week  and  months  be  modified  in  some  such  manner. 

*  The  writer  recalls  two  cases  in  which  the  failure  in  tests  which  involved 
the  application  of  training  was  very  significant.  The  first  was  that  of  a 
woman  of  about  30,  a  parole  patient  in  a  hospital  for  the  insane,  who  had 
never  shown  any  marked  symptoms  other  than  a  history  of  intellectual  in- 
feriority. This  patient  passed  practically  all  of  the  Binet  tests  in  the  IX, 
X  and  XII  year  groups,  but  failed  completely  in  the  test  of  making  change. 
This  observation  was  later  checked  up.  Another  case  of  a  woman  of  22, 
in  the  same  hospital,  presented  a  border-line  psychoneurotic  picture  perhaps, 
but  no  marked  symptoms  other  than  a  history  of  intellectual  inferiority.  She 
passed  in  a  great  many  of  the  difficult  tests  in  the  upper  years  but  had  great 
difficulty  in  telling  time.  Both  cases  had  lived  under  very  good  home  con- 
ditions and  had  mingled  with  people  of  ability.  A  great  many  tests  of  capa- 
city were  given,  but  the  most  illuminating  evidence  of  their  mental  status 
came  from  the  two  tests  mentioned. 


62  CARL  C.  BRIGHAM 

Comparing  the  conclusions  of  this  study  with  other  investiga- 
tions, the  agreement  is  fairly  close.  Schmitt's  results  do  not 
support  her  suggestion  that  the  definitions  test  relates  to  specific 
school  instruction.  The  other  tests  which  she  refers  to  this 
factor  (stamps,  date,  20  to  o,  change,  months  and  money)  show 
the  influence  to  a  marked  extent.  Binet  in  classifying  some  of 
the  tests  referred  the  tests  of  copying  a  sentence,  reading  for 
memories,  writing  from  dictation,  copying  a  diamond,  counting 
backwards  and  making  change  to  scholastic  training.  The  first 
three  tests  were  not  included  in  this  investigation.  The  diamond 
test  showed  the  influence  of  age  to  be  as  great  if  not  greater  than 
that  of  school  training.  The  last  two  tests  showed  a  marked 
influence  of  training.  Binet  referred  the  tests  of  counting  13 
pennies,  naming  four  colors,  naming  the  days  of  the  week  and 
enumerating  the  months  to  home  training.  The  last  two  showed 
a  marked  influence  of  school  training.  The  results  of  the  present 
investigation  agree  with  those  of  Chotzen  in  finding  no  efifect  or 
very  little  effect  of  training  in  the  tests  of  copying  the  diamond, 
repeating  digits,  describing  pictures,  counting  13  pennies,  naming 
colors,  comparing  remembered  objects,  defining  in  terms  of  use 
and  superior  to  use,  and  in  finding  marked  influence  of  this 
factor  in  the  test  of  naming  the  days  of  the  week. 

The  methods  used  in  analysing  the  results,  especially  the  sec- 
ond method,  reveal  several  suggestive  relations  between  the 
tests  and  the  school  grades.  There  is  a  general  correlation  be- 
tween the  tests  and  the  grades,  a  correlation  that  is  very  necessary 
to  establish,  for  there  is  also  a  general  correlation  between  intelli- 
gence and  grade.  In  analysing  the  results  of  the  individual  tests 
by  comparing  the  results  of  subjects  of  the  same  age  in  different 
grades,  and  of  subjects  of  different  ages  in  the  same  grade 
(Table  7),  it  was  seen  that,  as  a  general  rule,  the  growth  in  any 
particular  ability  occurred  in  passing  from  grade  to  grade,  not  in 
passing  from  age  to  age  within  one  grade.  In  fact  in  only  half 
of  the  cases  in  which  the  subjects  of  two  ages  in  one  grade  may 
be  compared  do  the  older  subjects  make  records  that  are  higher 
than  those  of  the  younger  ones,  and  only  10%  of  these  gains  are 
over  20%.     If  the  groups  were  considered  to  be  equal  in  all 


VARIABLE  FACTORS  IM  THE  BINET  TESTS  63 

cases  in  which  their  records  were  within  10%  of  each  other, 
equality  occurs  in  exactly  50%  of  the  cases.  Of  the  remainder, 
20%  of  the  groups  were  lower,  while  in  only  30%  of  the  cases 
are  the  older  subjects  actually  higher  than  the  younger  subjects 
of  the  same  grade.  Some  of  the  cases  of  retrogression  could 
well  be  accidental,  but  they  occur  too  frequently  to  be  due 
entirely  to  chance. 

Applying  the  same  general  method  to  the  cases  in  which  groups 
of  the  same  age  but  in  different  grades  were  compared,  5%  of 
the  groups  in  a  higher  grade  showed  lower  scores,  the  results 
correspond  in  43%  of  the  cases,  while  52%  showed  definite 
improvement.  This  might  indicate  that  there  is  a  higher  correla- 
tion between  the  tests  and  grade  than  between  the  tests  and  age. 
The  fact  that  the  comparison  of  children,  of  different  ages  in  the 
same  grade  showed  the  older  children  making  lower  records  in 
20%  of  the  cases,  equal  records  in  50%  of  the  cases  and  higher 
records  in  only  30%,  would  confirm  the  general  diagnostic  value 
of  the  tests  if  Bonser's  interpretation  of  this  phenomena  is  cor- 
rect. Bonser  (12)  applied  various  sorts  of  reasoning  tests  to 
children  in  the  fourth,  fifth  and  sixth  school  grades.  In 
summarizing  the  results  of  the  tests  in  the  different  grades,  he 
says,  "In  the  contrast  with  grade  progress  and  progress  with  age, 
in  the  generally  superior  showing  made  by  the  younger  groups 
of  children  of  any  grade  when  contrasted  with  the  older  pupils 
of  the  grade,  and  in  the  fairly  substantial  percentage  of  pupils 
from  lower  grades  found  in  the  highest  quartile  of  ability  for  all, 
it  is  shown  that  native  capacity  is  measured  to  a  high  degree  by 
the  tests." 

In  conclusion,  the  results  shown  in  this  chapter  would  indi- 
cate a  correlation  between  the  individual  tests  studied  and  the 
school  grades,  this  correlation  being  high  enough  in  some  cases 
to  show  the  actual  eft'ect  of  training.  In  answer  to  the  general 
objection  that  since  one  demonstration  of  the  accuracy  of  the 
tests  rests  on  their  correlation  with  school  grades,  the  school 
grades  are  the  real  measure  of  intelligence  and  the  mental  tests 
superfluous,  it  is  only  necessar}'  to  point  out  that  intelligence  tests, 
besides  affording  the  opportunity  for  accurate  standardization, 


64  CARL  C.  BRIGHAM 

also  detect  the  subject's  potential  abilities  independent  of  his  past 
performance.  The  school  measure  indicates  mental  defect  in 
cases  of  gross  retardation,  but  it  does  not  indicate  exceptional 
ability. 

Schmitt's  contention  that  the  school  represents  a  standard 
environmental  situation,  and  a  measure  of  a  subject's  ability 
should  include  a  measure  of  the  adequacy  of  his  reaction  to  this 
situation,  is  well  founded.  It  is  not,  however,  a  criticism  of  the 
Binet  scale,  for  the  scale  aims  to  test  native  capacity.  At  the 
Buffalo  conference  (15)  on  the  Binet  scale,  the  following  ques- 
tion was  raised, — "What  is  it,  after  all,  that  the  scale  aims  to 
test?"  The  question  was  answered  by  "We  believe  that  current 
misconceptions  as  to  the  aim  of  the  scale  should  be  removed.  It 
is  not  intended  to  test  the  emotional  or  volitional  nature,  but 
primarily  intelligence  (judgment)."  To  this  list  might  be  added 
the  assertion  that  the  scale  was  not  intended  to  test  a  child's 
reaction  to  the  school  situation,  or  to  furnish  an  outline  for 
taking  a  record  of  his  life  history, 

Rogers  and  Mclntyre  (54)  would  also  have  mental  tests  in- 
clude tests  dependent  on  both  school  and  home  training.  This 
general  trend  of  present  day  discussion  is  a  reversion  to  Binet's 
1908  type  of  scale,  a  tendency  to  which  Binet  was  in  opposition. 
The  probable  solution  rests  in  eliminating  from  the  scale  the  tests 
involving  training,  and  in  constructing  a  standardized  scale  of 
another  sort  for  the  estimation  of  the  individual's  reaction  to  the 
school  situation  in  terms  of  the  length  of  time  that  he  has  met 
that  situation.  That  such  a  scale  is  not  a  matter  of  speculation 
is  shown  by  the  number  of  scales  now  on  the  market  for  measur- 
ing handwriting,  spelling,  composition,  arithmetical  ability,  etc. 
Tests  of  native  capacity  and  tests  dependent  on  school  and  en- 
vironmental training  cannot  be  standardized  on  the  same  basis,  for 
they  are  essentially  different  measures.  Measures  of  the  first  sort 
may  perhaps  be  correlated  with  age,  while  measures  of  the  other 
sort  can  be  correlated  only  with  opportunity. 


V.  SEX  DIFFERENCES 

The  investigators  who  have  studied  the  influence  of  sex  differ- 
ences on  the  Binet-Simon  tests  have  used  two  methods,  that  of 
comparing  the  "mental  ages"  or  total  scores  of  subjects  of  each 
sex,  and  that  of  comparing  the  per  cent,  that  the  subjects  of  each 
sex  pass  each  test.  The  first  method  throws  no  light  on  the 
individual  tests,  inasmuch  as  one  sex  may  be  superior  in  one 
test  and  inferior  in  another  so  that  the  total  score  will  balance 
the  influence  of  this  factor.  Inasmuch  as  the  scale  is  founded  on 
the  principle  that  sex  differences  do  not  exist,  it  is  important  to 
study  the  individual  tests,  and  to  determine  the  accuracy  of  this 
assumption. 

The  Princeton  data  are  available  for  a  study  of  this  sort.  352 
subjects  (187  boys  and  165  girls)  between  the  ages  6  and  12 
were  examined.  The  method  of  study  adopted  was  that  of  com- 
paring the  results  of  non-selected  boys  and  girls  of  each  age,  and, 
as  a  check  on  this  method,  of  comparing  the  results  of  selected 
boys  and  girls  of  four  ages. 

Inasmuch  as  the  subjects  of  each  chronological  age  are  dis- 
tributed over  a  range  of  one  year  (the  6  year  subjects  for  exam- 
ple being  distributed  from  6.0  to  6.9),  the  actual  average  age  of 
the  subjects  of  each  age  was  computed  to  make  sure  that  no 
differences  might  appear  due  to  the  chance  selection  of  subjects 
at  either  extreme.    These  averages  are  shown  in  Table  9. 

TABLE  9 
Actual  Average  Chronological  Age  of  Boys  and  Girls  in  Each  Age  Group. 


BOYS 

GIRLS 

Number  of 

Average  Age 

Number  of 

Average  Age 

Subjects 

(M.V.) 

Subjects 

(M.V.) 

Age 

6 

Zl 

6.58   (0.20) 

2Z 

6.51    (0.20) 

Age 

7 

29 

7.50   (0.29) 

31 

7.39   (0.26) 

Age 

8 

24 

8.48  (0.29) 

28 

8.48   (0.22) 

Age 

9 

20 

9.46  (0.27) 

22 

9.54  (0.26) 

Age 

10 

31 

10.46   (0.25) 

23 

10.37   (0.30) 

Age 

II 

28 

11.59   (0.22) 

20 

11.52   (0.27) 

Age 

12 

18 

12.43   (0.30) 

18 

12.57   (0.24) 

68  CARL  C.  BRIGHAM 

for  girls  0.S3  yr.  (from  9  to  10),  while  the  maximum  increase 
for  boys  is  1.13  yr.  (from  10  to  11),  and  for  girls  1.15  yr.  (from 
10  to  11).  A  more  marked  lack  of  regularity  in  the  growth  of 
scholastic  ability  from  year  to  year  as  measured  by  the  average 
grade  is  shown  in  Table  11,  no  increase  being  shown  by  the  12 
year  boys  over  the  11  year  boys,  while  the  10  year  boys  show  an 
increase  of  1.44  to  i.oi  grades  over  the  9  year  boys.  In  the  same 
way  the  10  year  girls  show  an  increase  over  the  9  year  girls  that 
is  nearly  three  times  that  of  the  7  year  girls  over  the  6  year  girls, 
while  the  increase  of  the  7  year  girls  over  the  6  year  girls  is 
twice  that  of  the  12  year  girls  over  the  11  year  girls.  These 
relations  indicate  that  the  selection  of  subjects  is  not  uniform  at 
each  age.  The  subjects  of  any  one  age  may  be  either  a  superior 
or  inferior  selection  of  all  children  of  that  age,  and  there  is  no 
reason  for  supposing  that  this  random  sample  of  superior  or 
inferior  subjects  of  any  age  will  correspond  to  a  similar  sampling 
of  the  subjects  of  the  opposite  sex  of  the  same  age. 

The  process  of  calculating  the  percentage  that  the  boys  and 
girls  of  each  age  pass  each  test  is  extremely  simple,  but  the 
conclusion,  that  the  differences  found  between  the  percentage 
passed  by  the  sexes  at  each  age  may  be  attributed  to  sex  differ- 
ences, is  not  justified  unless  all  the  variable  factors  are  known. 

A  previous  chapter  showed  variations  in  the  tests  due  to  the 
influence  of  the  personal  equation  of  the  experimenters.  To 
avoid  this  variable  influence,  only  those  tests  were  studied  that 
showed  that  they  were  free  from  the  influence  of  this  factor. 
Inasmuch  as  each  experimenter  examined  approximately  the  same 
number  of  boys  and  girls  of  each  age,  any  influence  of  this  factor 
would  be  equalized,  provided,  of  course,  that  there  were  no  differ- 
ences in  the  reaction  of  the  experimenters  to  the  two  sexes.  In 
the  detailed  study  of  the  design  test,  it  was  found  that  experi- 
menter C  was  more  lenient  in  marking  girls  than  boys.  The 
possibility  of  a  similar  interpretation  in  a  few  other  tests  was 
suggested,  but  not  demonstrated.  In  analysing  the  results  for 
sex  differences,  however,  the  possibility  of  such  an  interpretation 
must  be  kept  in  mind. 

Another  possible  source  of  error  is  that  due  to  incomplete  data. 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  69 

The  experimenters,  in  giving  the  tests,  would  give  only  those 
within  the  approximate  range  of  the  subject,  so  that  each  test 
would  be  given  to  a  superior  selection  of  children  below  the 
normal  range  of  the  test,  and  to  an  inferior  selection  of  subjects 
above  this  range,  a  process  tending  to  make  the  apparent  growth 
of  an  ability  less  than  the  probable  real  growth.  In  comparing 
the  results  of  the  sexes,  however,  it  is  not  necessary  to  have  ac- 
curate results  on  the  growth  of  an  ability,  but  results  which  have 
the  same  determining  factors.  If  the  experimenters  gave  the 
test  to  approximately  the  same  proportions  of  boys  and  girls  at 
each  age,  a  comparison  of  the  percentage  passed  is  legitimate, 
even  if  a  small  proportion  of  the  whole  group  were  actually 
tested,  for  the  proportion  would  include  the  same  selection  of 
subjects.  The  number  of  boys  and  girls  at  each  age,  and  the 
percentage  that  each  test  was  given  to  these  subjects  are  shown 
in  Table  12.  The  test  of  counting  13  pennies,  for  example,  was 
given  2,7  times  to  6  year  boys,  or  100%  of  the  possible  number 
of  times,  while  the  test  of  counting  from  20  to  o  was  given  27 
times  to  the  same  group,  or  73%  of  the  possible  number  of 
times.  Column  A  shows  the  total  number  of  times  each  test  was 
given  to  all  of  the  boys  and  girls.  Column  B  gives  the  average 
age  of  all  the  boys  and  girls  to  whom  each  test  was  given.  The 
average  given  in  this  case  is  not  the  actual  average  derived  from 
the  actual  chronological  age  of  each  subject  figured  in  tenths,  but 
the  weighted^  average,  the  whole  numbers  6,  7,  8,  9,  10,  11,  and 
12  being  used. 

Table  12  shows  a  very  close  correspondence  between  the  per- 
centage that  each  test  was  given  to  boys  and  girls  of  each  age,  so 
that  the  error  due  to  incomplete  data,  though  present,  is  present 
to  the  same  extent  in  the  results  of  both  sexes,  and  may  be 
disregarded.  A  fairly  close  correspondence  in  the  average  age 
of  all  the  boys  and  girls  to  whom  each  test  was  given  is  also 
indicated  in  Table  12.    In  the  test  of  counting  stamps  there  is  an 

^  For  example,  in  the  test  of  counting  13  pennies,  the  average  age  of  the 

boys  to  whom  the  test  was  given  is, — 

(37x6)  +  (28x7)  +  (i6x8)  +  (8x9)-K7xio)  +  (3xii)  +  (ixi2)  _  _„  ^^^^^ 
__ 7.33  years 


72  CARL  C.  BRIG  HAM 

Neither  method,  then,  is  entirely  satisfactory,  the  first  because 
it  would  tend  to  exaggerate  chance  differences,  the  second  because 
it  would  tend  to  obscure  real  dift'erences.  The  method  used  in 
this  study  is  that  of  comparing  the  results  of  non-selected  and 
selected  subjects  of  each  age  and  sex,  studying  first  the  general 
growth  of  each  ability  from  age  to  age  within  each  sex,  and  using 
the  per  cent,  that  all  subjects  pass  each  test  to  determine  the  cor- 
relation between  the  results  of  non-selected  and  selected  subjects. 

Table  13  shows  the  percentage  of  proportion^'''  that  the  boys  and 
girls  of  each  age  pass  each  test,  the  percentage  that  all  boys  and 
girls  pass  each  test,  the  actual  percentage  that  the  boys  are  su- 
perior to  (-J-)  or  inferior  to  ( — )  the  girls  of  each  age,  the  differ- 
ence between  the  average  age  of  all  boys  and  girls  to  whom  each 
test  was  given,  and  the  difference  between  the  percentage  that 
all  boys  and  girls  pass  each  test. 

The  dift'erences  between  the  performance  of  the  boys  and  girls 
at  each  age  have  no  meaning  unless  the  general  growth  of  the 
abilities  in  each  sex  is  first  understood.  Studying  first  the  re- 
sults of  the  187  non-selected  boys  shown  in  the  first  seven 
columns  of  Table  13,  it  may  be  seen  that  the  growth  of  ability 
in  each  test  is  rather  irregular.  The  test  of  naming  the  months, 
for  example,  shows  a  slight  decrease  from  9  to  12.  The  differ- 
ences between  the  percentage  performances  of  the  subjects  of 
each  age  and  those  of  the  preceding  age  were  calculated.     The 

12  year  group,  compared  to  the  11  year  group,  is  -\-ii%  on  the 
test  of  giving  the  date,  — 9%  on  the  test  of  naming  the  months 
etc.  61  differences  were  thus  obtained,  varying  in  magnitude 
from  — 15%  to  +36%,  the  median  being  +8%   (Q^975%)- 

13  of  the  deviations  (21  % )  were  minus  values.  The  largest  nega- 
tive deviations  occurred  in  the  tests  of  naming  colors  ( — 15%,  7 
to  8),  naming  money  ( — 15%,  n  to  12),  and  constructing  a 
sentence  containing  two  ideas  ( — 13%,  8  to  9).  The  remaining 
10  minus  deviations  were  less  than  10%. 

^  The  proportion  given  is  the  number  of  times  a  test  was  given  over  the 
number  of  times  a  test  was  passed.  No  percentages  were  calculated  for 
tests  given  less  than  12  times,  and  no  percentages  are  given  for  the  defini- 
tions tests  on  account  of  the  small  number  of  times  they  are  given  to  all 
subjects. 


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74  CARL  C.  BRIGHAM 

An  index  of  the  growth  from  year  to  year  was  obtained  by 
calculating-  the  average  percentage  increase  from  one  age  group 
to  another.  For  example,  the  7  year  boys  were  26%  higher  than 
the  6  year  boys  in  the  test  of  naming  colors,  5%  higher  in  naming 
the  date  etc.  The  average  of  the  10  possible  comparisons  between 
6  and  7  year  boys  shows  that  the  latter  averaged  16.1%  higher 
than  the  former.  The  average  increases  in  percentage  passed 
from  year  to  year  are  as  follows, — 6  to  7=16.1%  ;  7  to  8=13.5% 
8  to  9=8.7%;  9  to  10=11.2%;  10  to  11=6.0%;  and  11  to 
12=0.2%.  These  figures  show  strikingly  the  irregularity  of 
the  growth  from  age  to  age.  Comparing  these  average  percent- 
age increases  in  tests  with  the  averages  shown  in  Tables  9  and  11, 
there  is  no  observable  relation  between  this  increase  and  the  in- 
crease in  average  age  from  age  to  age,  or  the  increase  in  average 
grade  from  age  to  age.  The  smallest  increase  in  the  tests 
(0.2%,  II  to  12)  coincides  with  the  smallest  increase  in  average 
age  from  year  to  year  (0.84  yr.),  and  the  smallest  increase  in 
average  grade  from  year  to  year.  The  other  relations  are 
varied. 

The  fact  of  the  variability  in  the  results  of  the  non-selected 
boys  stands  out.  The  irregularity  of  the  growth  of  the  various 
abilities,  and  the  fact  that  in  21%  of  the  cases  the  boys  of  one 
age  are  actually  lower  than  those  of  the  previous  age,  point  to 
the  conclusion  that  certain  allowances  will  have  to  be  made  for 
chance  variations.  It  is  not  possible  to  acccount  for  the  varia- 
tions in  growth  by  reference  to  the  relative  increase  in  average 
age  or  average  grade  from  year  to  year. 

The  results  of  the  165  non-selected  girls,  shown  in  italics  in 
the  first  seven  columns  of  table  13,  were  studied  in  the  same 
manner  as  the  results  of  the  boys.  60  differences  between  the 
percentage  performance  of  the  girls  of  each  age  and  those  of 
the  preceding  age  were  obtained.  These  differences  ranged  from 
—2>Z%  to  +50%,  the  median  being  7%  (Qr=8%).  10  of  the 
deviations  (17%),  were  minus  values.  The  largest  deviations 
were  shown  in  the  tests  of  naming  60  words,  ( — 33%,  11  to  12), 
counting  stamps    ( — 20%,    9    to    10),    and    drawing    designs 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  75 

( — 14%,  8  to  9).  The  remaining  7  minus  deviations  were  below 
10%. 

The  average  increases  in  the  percentage  passed  from  year  to 
year  are  as  follows, —  6  to  7=3.9%;  7  to  8=15%;  8  to  g= 
8.8%;  9  to  10=10.1%;  10  to  11=8.7%;  II  to  12=1.8%.  Both 
boys  and  girls  show  the  smallest  average  increase  in  the  percent- 
age passed  in  the  step  from  11  to  12,  and  the  magnitudes  of  the 
increases  agree  fairly  well  except  for  the  step  from  6  to  7.  The 
increase  of  the  7  year  girls  over  the  6  year  girls  is  3.9%,  the 
next  to  the  smallest  increase  of  one  age  group  over  any  preceding 
group.  The  7  year  boys,  however,  show  an  average  increase  of 
16.1%,  over  the  6  year  boys,  the  largest  increase  of  any  group 
of  boys  over  any  preceding  group.  It  will  be  difficult,  then,  to 
draw  conclusions  concerning  sex  differences  from  a  comparison 
of  the  6  year  boys  and  girls,  for  the  6  year  girls  are  either  a 
superior  selection  or  the  6  year  boys  are  an  inferior  selection 
if  the  character  of  these  groups  be  judged  by  the  comparison 
with  the  7  year  subjects.  The  same  comparison,  on  the  other 
hand,  might  indicate  that  the  7  year  girls  were  an  inferior  se- 
lection and  the  7  year  boys  a  superior  selection  from  the  general 
run.  It  is  only  possible  to  point  out  the  irregularity,  however,  it 
is  not  possible  to  show  the  cause  of  the  irregularity. 

A  comparison  of  the  average  increase  in  the  percentage  passed 
by  girls  from  age  to  age  with  the  increase  in  the  average  ages 
shown  in  Table  9  shows  no  demonstrable  relation  to  exist.  Com- 
paring this  growth  in  the  ability  on  the  tests  with  the  growth  in 
average  grade,  shown  in  Table  11,  shows  a  very  positive  relation 
to  exist  between  these  factors.  Where  the  increase  in  average 
grade  is  smallest  (i.e.  from  6  to  7  and  from  11  to  12),  the  in- 
crease in  the  tests  is  smallest  (3.9%  and  1.8%),  while  the  great- 
est increase  in  grade  (from  9  to  10  and  from  7  to  8)  coincide 
with  the  greatest  increase  in  the  test  abilities  (10.1%  and 
15.0%).  This  relation  was  not  indicated  in  the  results  of  the 
boys.  The  explanation  of  this  fact  that  a  correlation  between 
the  increase  in  the  tests  with  grade  was  found  in  the  results  of 
the  girls  but  not  of  the  boys  is  a  matter  of  speculation.  It' has 
been  shown  that  the  boys  have  a  higher  variability  in  grade  than 


76  CARL  C.  BRIGHAM    ■ 

girls.  This  tendency  of  the  boys  to  be  distributed  in  a  wider 
range  of  grades  might  nullify  the  grade  correlation  slightly, 
but  probably  not  to  any  considerable  extent.  The  fact  that  the 
causes  of  this  variation  are  not  determined  serves  to  illustrate 
the  dangers  of  comparing  the  results  of  two  groups  when  the 
factors  operating  on  the  groups  are  not  known. 

The  foregoing  study  of  the  growth  of  the  various  abilities 
from  age  to  age  in  each  sex,  and  the  analysis  of  the  causes  in- 
fluencing this  growth,  demonstrates  the  great  variability  of  the 
results.  This  fact  of  variability  must  be  considered  before  draw- 
ing conclusions  concerning  sex  differences  by  the  method  of 
comparing  the  results  of  boys  and  girls  of  each  age. 

The  percentage  differences  between  the  performance  of  non- 
selected  boys  and  girls  of  each  age  are  shown  in  Table  13.  In 
actual  magnitude,  these  differences  vary  from  0%  to  36%,  the 
median  being  9%  (Q=5.5%).  75%  of  the  differences  are 
17%  or  under,  and  only  16%  are  over  20%.  In  regard  to  sign, 
the  differences  vary  from  — 36%  to  +26%,  the  median  being 
— 3.5%  (Q=8.75%),  showing  a  slight  general  superiority  of 
the  girls.  If  the  number  of  possibilities  of  variation  in  compar- 
ing the  results  of  small  groups  of  non-selected  subjects  are 
taken  into  consideration,  the  presence  of  mental  defectives,  of 
subjects  having  language  difficulties,  of  subjects  in  different 
grades  influenced  by  different  training,  the  possibility  of  a  super- 
ior selection  of  subjects  at  one  age  group  than  at  another,  and  the 
probability  that  similar  chance  samplings  would  not  fall  at  the 
same  age,  the  fact  of  correspondence  indicated  in  Table  13  has 
more  meaning  than  the  fact  of  divergence. 

The  variability  indicated  in  the  study  of  the  growth  of  abilities 
with  age  was  so  great  that  it  makes  interpretation  of  the  results 
in  terms  of  sex  differences  very  difficult,  and  warranted  conclu- 
sions impossible.  It  is  legitimate  to  expect  that  the  older  subjects 
of  either  sex  should  make  higher  scores  than  the  younger  sub- 
jects of  the  same  sex,  but  this  was  not  found  to  be  the  universal 
rule.  The  boys'  results  showed  minus  deviations  in  21%  of  the 
cases  and  the  girls'  results  showed  minus  deviations  in  17%  of 
the  cases.     In  one  case  the  12  year  girls  were  33%  lower  than 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  77 

the  II  year  girls.  If  this  value  (33%)  be  taken  as  the  error  due 
to  chance  variation,  then  only  one  value,  that  of  — 36%,  (naming 
the  months,  age  12),  may  be  taken  as  significant,  and  it  has  been 
seen  that  in  this  test  the  12  year  boys  are  10%  lower  than  the  9 
year  boys.  The  conclusion  would  follow,  then,  that  there  were 
no  sex  differences.  This  alternative,  however,  seems  to  place  too 
much  weight  on  one  variation  so  that  the  truth  probably  lies  in 
the  assertion  that  the  sex  differences,  that  actually  exist,  are 
slight. 

A  study  of  the  reactions  of  selected  groups  of  boys  and  girls 
should  throw  light  on  the  results  from  non-selected  subjects,  and 
make  conclusions  more  certain.  Subjects  were  selected  by  a 
process  of  elimination  and  selection.  All  of  the  subjects  that 
were  in  the  special  class  and  minus  grades  were  eliminated,  along 
with  all  children  of  non-English  speaking  parents.  From  the 
following  group  of  English  speaking  subjects  in  the  regular 
grades  all  subjects  were  eliminated  who  had  entered  grade  at  an 
age  very  much  above  or  below  that  of  the  general  run  of  en- 
trants.* The  remaining  subjects  ranged  in  age  from  4.3  years 
to  14.4  years,  but  were  found  to  group  rather  closely  around 
certain  ages.  It  was  possible  to  find  four  groups  of  boys  and 
girls  of  approximately  the  same  chronological  ages.  The  char- 
acter of  these  subjects  is  indicated  in  Table  14. 

The  four  groups  of  subjects,  chronologically  from  6.0  to  6.9, 
7.6  to  8.9,  9.7  to  10.9  and  11.7  to  13.3  (which  will  be  referred 
to  as  6,  8,  10  and  12),  were  distributed  in  approximately  the 
same  grades,  and  had  approximately  the  same  average  age  and 
average  grade.  The  results  of  these  groups  are  shown  in  Table 
15,  which  is  arranged  to  show  all  the  facts  for  selected  subjects 
that  were  given  for  non-selected  subjects  in  Tables  12  and  13. 
The  first  four  columns  show  the  percentage  that  each  test  was 
given  to  each  group.  The  next  four  columns  show  the  percentage 
or  the  proportion  that  the  subjects  in  each  group  passed  each 

*  The  ages  on  entering  each  grade  of  the  subjects  retained  were  as  fol- 
lows,— Kindergarten  =  4,  5  and  6;  Grade  I  =  5,  6  and  7;  Grade  II  =  6,  7 
and  8;  Grade  III  =  8,  9  and  10;  Grade  IV  =  9,  10  and  11;  Grade  V  =  ro, 
II  and  12;  Grade  VI  =  11,  12  and  13. 


7^  CARL  C.  BRIGHAM 

TABLE  14 

Age  in  Grade  Distribution,  Average  Grade  and  Average  Age  of  167  Selected 

Subjects.    86  Boys  and  81  Girls. 

Age  in  Grade  Distribution 


Age  Group 

Sex 

K 

I 

II  III 

IV 

V 

VI  TOTAL  Average 

Average 

Grade  (M.V.)  Age  (M.V.) 

6.0  to   6.9 

Boys 

5 

13 

18 

0.72  (0.40) 

6.52  (0.22) 

Girls 

3 

13 

2 

18 

0.89  (0.39) 

6.53  (0.22) 

7.6  to   8.9 

Boys 

7 

13     3 

23 

1.83  (0.51) 

8.09  (0.38) 

Girls 

2 

13     5 

20 

2.15  (0.43) 

8.32  (0.38) 

9.7  to  10.9 

Boys 

6 

12 

2 

20 

3.80  (0.48) 

10.37  (0.36) 

Girls 

9 

7 

5 

21 

3.8i  (0.69) 

10.14  (0.32) 

11.7  to  13.3 

Boys 

2 

8 

15 

25 

5.52  (0.58) 

12.35  (0.55) 

Girls 

3 

8 

II 

22 

5.36  (0.64) 

12.41  (0.46) 

test.  Column  A  shows  the  total  number  of  times  each  test  was 
given  to  all  boys  and  girls,  Column  B,  the  weighted  average  age 
(the  average  ages  given  in  Table  14  being  used),  and  Column  C 
the  percentage  that  all  subjects  passed  each  test.  The  next  four 
columns  show  the  percentage  that  the  boys  are  above  (  +  )  or 
below  ( — )  the  girls.  Column  D  (derived  from  Column  B), 
gives  the  difference  between  the  average  ages  of  all  subjects  to 
whom  each  test  was  given.  Column  E  (derived  from  Column 
C),  gives  the  differences  between  the  percentages  passed  by  all 
boys  and  girls  on  each  test. 

The  growth  of  the  various  abilities  with  age  in  the  selected 
groups  of  subjects  is  more  uniform  than  that  shown  by  the  non- 
selected  subjects.  Only  three  cases  appear  in  which  the  younger 
subjects  make  higher  scores  than  those  of  older  subjects,  these 
exceptions  occurring  in  the  tests  of  describing  pictures  ( — 3%, 
girls  6  to  8),  naming  colors  ( — 7%,  girls  6  to  8),  and  naming 
months  ( — 9%,  boys,  10  to  12).  In  the  comparison  of  the 
sexes  41  differences  are  obtained  varying  in  magnitude  from 
— 28%  to  +26%,  the  median  being  0%  {Q=g.t^%).  In  actual 
magnitude  the  differences  vary  from  o  to  28,  the  median  being 
10%  (Q^475%),  the  median  being  1%  higher  than  that  of 
non-selected  data,  and  the  variability  0.75%  less.  75%  of  the 
differences  were  less  than  14%. 


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8o  CARL  C.  BRIGHAM 

The  change  of  the  median  of  the  series  of  differences  from 
— 3-5%  (non-selected)  to  o%  (selected)  shows  that  the  elimina- 
tion of  over  age  and  special  grade  pupils  has  helped  the  boys 
more  than  the  girls,  and  has  altered  the  general  relations  between 
the  sexes.  This  fact  is  also  indicated  by  the  average  difference 
in  the  percentages  that  all  subjects  pass  each  test,  the  average  for 
non-selected  subjects  being  — 14%  and  for  selected  subjects 
4-1.6%,  The  non-selected  boys  from  6  to  12  were  given,  in  all, 
2436  tests,  these  tests  being  passed  60.8%  of  the  time.  The 
non-selected  girls  were  given  2195  tests,  passing  61.6%,  the 
advantage  being  0.8%  in  their  favor.  The  selected  boys  were 
given  1 125  tests,  passing  64.3%,  an  advantage  of  0.1%  over  the 
girls  who  passed  64.2%  of  1034  tests.  The  foregoing  changes 
indicate  clearly  that  the  selection  of  subjects  has  changed  the 
general  relations  between  the  sexes,  helping  the  boys  more  than 
the  girls. 

The  relations  between  the  results  of  selected  and  non-selected 
subjects  may  be  studied  by  a  comparison  of  the  differences  be- 
tween the  percentages  passed  by  all  subjects.  If  the  differences 
between  the  scores  of  the  boys  and  girls  are  due  to  but  one 
factor,  that  of  sex  differences,  then  the  correlation  between  the 
two  methods  of  study  should  be  very  nearly  absolute.  The  cor- 
relation (Pearson  product-moments  formula)  between  the  dif- 
ferences in  the  percentage  passed  by  all  boys  and  girls  according 
to  the  two  methods  is  0.726  (pe=o.o75).  This  correlation  be- 
tween the  two  methods  is  high,  but  it  would  probably  be  high 
inasmuch  as  the  167  selected  subjects  are  included  in  the  352 
non-selected  subjects.  The  results  of  the  two  methods  show  cer- 
tain large  discrepancies.  The  changes  of  the  greatest  magnitude 
are  those  shown  by  the  60  words  test  (-1-4%  by  the  first  method 
to  -j-  18%  by  the  second),  the  tests  of  defining  in  terms  superior 
to  use  (+7%  to  -f-2i%),  of  naming  the  days  of  the  week, 
( — 16%  to  — 2%),  giving  rhymes,  ( — 10%  to  -|-i%),  naming 
colors,  ( — 14%  to  ' — 4%),  copying  the  diamond,  (  +  1%  to 
— 8%),  and  counting  from  20  to  o  ( — 8%  to  — 16%), 
The  comparison  of  the  median  differences  shows  that 
the  selected  method  tends  to  improve  the  results  of  the  boys  more 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  8i 

than  those  of  the  girls.  All  of  the  changes  in  the  results  of  the 
two  methods  are  not  in  favor  of  the  boys,  however,  the  total 
scores  on  the  diamond  and  20  to  o  tests  showing  changes  in 
favor  of  the  girls.  If  the  cause  of  the  variations  shown  by  the 
first  method  is  the  presence  of  a  few  children  of  non-English 
speaking  parents,  to  special  class  and  minus  grade  children,  then 
the  elimination  of  this  source  of  error  should  change  the  results 
in  only  one  direction. 

The  analysis  of  the  results  of  selected  subjects,  therefore,  does 
not  lessen  the  difficulty  of  the  interpretation  of  the  results  in 
the  light  of  sex  differences.  The  rate  of  growth  of  the  various 
abilities  with  age  is  irregular.  The  analysis  of  the  irregularities 
points  to  the  fact  that  the  boys  or  girls  of  any  age  may  be  a 
chance  selection  of  superior  or  inferior  subjects  at  that  age.  The 
method  of  comparing  selected  subjects  would  tend  to  eliminate 
the  inferior  selection  of  subjects,  but  would  not  eliminate  the 
possibility  of  a  superior  selection. 

The  comparison  of  the  results  of  the  sexes  shows  differences 
at  certain  ages  and  on  certain  tests  that  are  as  high  as  20%. 
The  problem  involved  is  that  of  deciding  whether  these  large 
differences  are  due  to  chance  or  to  differences  in  the  reactions 
of  the  sexes.  Certain  tests  show  large  deviations  first  in  favor 
of  one  sex  and  then  in  favor  of  the  other.  If  a  difiference  of  a 
percentage  of  any  magnitude  on  any  test  is  to  be  attributed  to  a 
sex  difference,  then  the  same  line  of  reasoning  will  show  that  in 
certain  tests  the  abilities  change  from  one  sex  to  the  other.  The 
analysis  of  the  tests  that  show  this  crossing  of  ability  should 
throw  light  on  the  other  tests. 

Three  tests  show  substantial  differences  in  favor  of  both  sexes 
according  to  both  methods.  In  the  test  of  copying  the  diamond, 
the  non-selected  girls  lead  at  the  start,  age  6,  and  the  boys  are 
ahead  at  7,  8  and  9,  the  same  relations  being  shown  by  selected 
subjects  of  6  and  8.  In  the  test  of  copying  the  designs  from 
memory,  the  non-selected  girls  are  24%  below  the  boys  at  age  9 
and  21%  above  the  boys  at  age  12,  the  same  relations  being 
shown  by  the  selected  subjects  of  10  and  12.  In  the  test  of 
naming  60  words  in  three  minutes,  the  non-selected  girls  are 


82  CARL  C.  BRIGHAM 

19%  above  the  boys  at  9,  and  19%  below  at  12.     The  selected 
boys  of  ID  and  12  are  in  advance  of  the  girls  in  this  test. 

These  three  tests  are  crucial  in  the  consideration  of  the  prob- 
lem of  whether  differences  shown  between  the  boys  and  girls  are 
due  to  actual  sex  differences  or  due  to  accidental  causes.  Each  of 
these  tests  may  be  studied  by  a  method  more  accurate  than  that  of 
comparing  the  percentage  passed  at  each  age.  The  reproductions 
of  the  diamond  were  arbitrarily  sorted  in  six  groups  according 
to  their  merits  by  a  method  described  in  the  discussion  of  the 
personal  equation.  The  first  group  contained  the  best  repro- 
ductions, the  sixth,  the  poorest.  The  reproductions  of  the 
designs  were  graded  from  o  to  20  by  an  arbitrary  point  system 
described  under  the  discussion  of  the  personal  equation.  A 
measure  of  the  ability  in  the  60  word  test  is  the  actual  number  of 
words  given  in  three  minutes,  a  measure  recorded  by  the  experi- 
menters in  each  case.  Table  16  shows  the  average  score  made 
by  the  non-selected  and  selected  boys  and  girls  of  each  age  in 
these  three  tests. 

TABLE  16 
Average  Score  (Mean  Variation)  of  Subjects  of  Each  Age  on  Three  Tests. 

Copying  the  Diamond  Drawing  the  Designs  Naming  60  words 

Average  Group  of  Average  number  of  Average  number  of  words 

the  Reproductions.                points  scored.  given  in  three  minutes. 

M             Boys          Girls                 Boys             Girls  Boys  Girls 
"I   6   4.27(1.28)  3.57(1-24) 
■-f    7   2.85(1.04)  3.17(1.37) 

^    8   2.20(1.15)  3.24(1.57)  8.06(6.19)    9.00(5.25) 

^    9    2.33(0.89)  3.00(1.29)  10.29(5.30)    5.32(4.61)  52.93(11.20)  59.91(10.10) 

^  10  9-17(5.33)    9.18(6.73)  68.12(13.12)  61.76(11.25) 

i  II  8.64(6.73)  10.94(7-06)  73-65(13-35)  71-28(14.25) 

=  12  8.64(6.02)  11.08(6.08)  68.75(12.28)  58.14(12.57) 

•0^6   4.27(1.20)  3.33(1.26) 
"C.J.    8   2.32(1.00)  3.00(1.17) 

"S  S  10  9-S5(S-6o)    7-29(6.42)      67-31(12.74)62.13(11.39) 

12  12.53(5-38)  13.56(5.55)       75.33(10.92)  66.84(13.87) 

The  relations  indicated  by  the  percentage  passed  are  also  indi- 
cated by  the  more  reliable  method  of  comparing  the  average 
scores.  In  the  test  of  copying  the  diamond,  the  6  year  non- 
selected  girls  average  0.70  group  better  than  the  boys,  while  the 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  83 

selected  girls  are  0.94  ahead.  The  comparison  of  the  7,  8  and  9 
year  subjects  shows  the  boys  ahead  in  all  cases,  the  8  year  non- 
selected  boys  averaging  over  one  group  higher.  The  non-selected 
boys  show  an  improvement  of  two  groups  from  6  to  9,  while  the 
girls  show  an  improvement  of  only  half  a  group.  One  sex  shows 
a  decided  growth  of  ability,  the  other  practically  none.  If  the 
differences  indicated  are  to  be  taken  as  real,  it  will  be  necessary 
to  assume  that  the  girls  pick  up  the  ability  to  draw  a  diamond 
easier  than  the  boys,  but  that  this  ability  once  obtained  remains 
constant — that  the  effect  of  maturity  operates  on  one  sex  but 
not  on  another.  The  number  of  cases  on  which  this  assumption 
is  based  (174  subjects  from  6  to  9)  is  so  small,  and  the  chances 
of  variation  in  the  selection  of  subjects  of  different  intellectual 
status  in  each  age  group  is  so  large,  that  the  assumption  is  not 
substantiated. 

The  relations  indicated  in  the  test  of  copying  the  designs  are 
more  variable  than  those  of  the  diamond  test.  The  9  year 
non-selected  boys  show  an  improvement  over  the  8  year  boys,  but 
from  9  to  12  there  is  a  gradual  decrease  in  the  ability,  so  that 
the  1 1  and  12  year  boys  are  only  slightly  ahead  of  the  8  year  boys. 
The  relations  shown  by  the  non-selected  girls  are  exactly  the 
reverse  of  those  of  the  boys.  The  9  year  girls  are  very  much 
lower  than  the  8  year  girls,  and  a  gradual  increase  appears  from 
9  to  12  instead  of  a  decrease.  The  comparison  of  these  opposite 
relations  gives  a  maximum  difference  in  favor  of  the  boys  at  9 
and  the  girls  at  12.  If  the  relations  indicated  in  this  test  are  to  be 
considered  definite,  the  assumption  is  involved  that  the  influence 
of  increasing  age  on  one  sex  is  exactly  opposite  to  that  on  the 
other  sex,  an  assumption  that  is  not  substantiated  in  view  of  the 
small  number  of  cases  (183  subjects  from  8  to  12)  and  the  possi- 
bility of  selecting  subjects  of  chance  superiority  in  the  small 
groups  at  each  age. 

The  relations  indicated  in  the  test  of  naming  60  words  are 
more  constant  than  those  shown  in  the  diamond  or  design  tests. 
Both  sexes  show  a  growth  of  ability  from  9  to  1 1  and  a  decrease 
from  II  to  12.  The  growth  is  irregular,  however,  the  girls 
showing  less  growth  from  9  to  10,  and  a  greater  drop  from  11  to 


84  CARL  C.  BRIGHAM 

12,  SO  that  a  comparison  of  the  sexes  shows  a  deviation  in  favoi 
of  the  girls  at  9  and  of  the  boys  at  12.  The  assumption  of  any- 
large  sex  differences  in  this  test  involves  the  assumption  that  12 
year  girls  have  less  ability  in  this  test  than  9  year  girls,  and  that 
the  influence  of  maturity  operates  differently  on  the  two  sexes, 
an  assumption  that  is  not  substantiated  in  view  of  the  many  varia- 
ble factors. 

The  conclusion  that  a  definite  crossing  of  ability  between  the 
sexes  occurs  in  the  tests  of  copying  the  diamond,  copying  designs 
and  naming  60  words,  is  not  substantiated.  It  is  not  justifiable 
to  attribute  a  difference  of  20%  between  the  sexes  to  a  real  sex 
difference  on  one  test  and  not  on  another.  If  the  differences 
shown  between  the  results  of  the  sexes  in  the  tests  of  constructing 
a  sentence  containing  one  idea,  of  naming  the  months,  naming 
the  days  of  the  week,  counting  stamps  and  naming  colors  are 
to  be  attributed  to  sex  differences,  then  the  variations  in  ability 
shown  in  the  diamond,  design  and  60  word  test  must  be  assumed 
to  be  definite.  These  assumptions  were  not  found  to  be  sub- 
stantiated, however,  so  that  it  is  not  possible  to  draw  any  con- 
clusions concerning  sex  differences  from  a  study  of  the  percent- 
age that  selected  or  unselected  subjects  of  each  age  pass  each 
test. 

The  variable  influences  due  to  the  selection  of  subjects  of 
different  status  at  each  age  are  eliminated  or  counterbalanced  to 
some  extent  by  combining  the  subjects  of  all  ages.  The  differ- 
ences between  the  percentages  that  all  boys  and  girls  pass  each 
test  are  to  some  extent  influenced  by  the  ages  of  the  subjects  to 
whom  each  test  was  given.  The  correlation  (Pearson  product- 
moments  formula)  of  the  differences  between  the  percentages 
that  all  non-selected  boys  and  girls  passed  each  test  with  the 
difference  between  the  average  ages  of  all  the  non-selected  boys 
and  girls  to  whom  each  test  was  given  is  0.394  (pe=o.i34).  The 
correlation  between  the  same  arrays  from  selected  subjects  (i.e. 
between  Columns  D  and  E  of  Table  15)  is  0.388  (pe=o.i35). 
These  correlations  between  the  tests  and  age  are  high  enough  to 
indicate  that  the  factor  of  age  is  present  to  some  extent.  The 
close  correspondence  in  the  correlations  from  the  two  methods 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  85 

indicates  that  the  age  factor  is  present  to  the  same  extent  in  both 
methods.  The  tests  vary  in  the  degree  with  which  they  correlate 
with  age,  so  that  it  is  not  possible  to  estimate  the  amount  of  the 
influence  of  this  factor.  Furthermore,  it  has  been  seen  that  the 
results  from  the  two  methods  are  not  in  strict  accordance,  that 
the  elimination  of  inferior  subjects  caused  changes  in  the  results 
in  both  directions.  For  these  reasons,  it  is  not  possible  to  draw 
any  conclusions  concerning  sex  differences  from  a  comparison 
of  the  percentages  passed  by  all  subjects. 

Certain  negative  conclusions  are,  however,  possible.  The  num- 
ber of  subjects  at  each  age  in  both  methods  is  comparatively 
small.  The  chances  of  variations  due  to  factors  other  than  sex 
differences  has  been  shown  to  be  very  large.  The  fact  of  corres- 
pondence between  the  results  of  the  two  sexes  is  therefore  of 
more  importance  than  the  fact  of  divergence.  75%  of  the  differ- 
ences between  the  non-selected  boys  and  girls  are  iy%  or  under, 
while  the  same  proportion  of  the  differences  between  selected 
boys  and  girls  falls  under  14%.  If  it  is  assumed  that  the  subjects 
of  any  age  should  not  test  lower  than  those  of  any  preceding  age, 
and  allowance  is  made  for  differences  between  the  sexes  that  are 
exaggerated  on  account  of  the  chance  falling  off  of  ability  with 
older  subjects,  only  9%  of  the  differences  between  the  non- 
selected  boys  and  girls  are  over  20%  (derived  from  Table  13). 

The  evidence  from  the  foregoing  methods  of  study  points  to 
the  conclusion  that  the  sex  differences,  if  present,  are  under  20% 
or  25%  as  a  maximum,  and  that  deviations  of  this  magnitude 
are  marked  exceptions  to  the  general  run  of  differences.  The 
conclusion  that  the  differences  that  might  possibly  be  attributed 
to  the  sex  factor  are  slight,  has  no  meaning  unless  the  word 
"slight"  is  defined  independently  of  the  writer's  personal  opinion. 
The  differences  shown  between  the  results  of  the  sexes  are 
smaller  than  those  that  were  attributed  to  the  factor  of  the  per- 
sonal equation  in  the  study  of  the  results  of  the  four  experi- 
menters. It  was  concluded  that  certain  tests  were  influenced  by 
grade  training.  These  tests  showed  from  40%  to  60%  improve- 
ment from  one  grade  to  another,  so  that  the  greatest  influence 
that  may  be  attributed  to  the  sex  factor  is  only  approximately 


86  CARL  C.  BRIGHAM 

one  half  that  due  to  grade  training.  The  following  study  of  the 
diagnostic  value  of  the  tests  will  show  that  the  deviations  that 
might  be  attributed  to  the  sex  factor  are  insignificant  when  com- 
pared to  the  differences  between  the  reactions  of  normal  and  re- 
tarded children  to  the  individual  tests. 

Most  of  the  investigators  who  have  studied  the  factor  of  sex 
differences  in  the  Binet  tests,  have  studied  them  from  the  stand- 
point of  the  "mental  ages"  or  total  scores  made  by  the  subjects 
of  both  sexes.  A  few  investigators  have  studied  sex  differences 
in  the  light  of  the  individual  tests.  Descoeudres  (20)  reports  the 
results  of  the  application  of  the  Binet  tests  to  24  subjects,  one 
good  and  one  poor  pupil  of  each  sex  from  each  of  six  school 
grades,  drawing  conclusions  from  this  investigation  concerning 
the  diagnostic  value  of  the  individual  tests  and  the  sex  differences 
involved.  Obviously  the  number  of  subjects  is  too  small  to 
allow  any  conclusions  to  be  drawn.  Chotzen  (18)  compared  the 
percentage  that  all  feeble-minded  boys  and  girls  passed  each  of 
15  tests,  finding  differences  varying  in  magnitude  from  1%  to 
20%.  The  largest  deviations  were  those  of  20%  in  favor  of 
the  boys  in  the  test  of  copying  the  diamond,  13%  in  favor  of  the 
girls  in  the  test  of  executing  three  commissions,  12%  in  favor 
of  the  boys  in  naming  the  pieces  of  money,  11%  in  favor  of  the 
girls  in  the  test  of  repeating  a  sentence  of  16  syllables,  and  10% 
in  favor  of  the  girls  in  detecting  omissions  in  pictures.  All  other 
differences  were  less  than  10%. 

Bloch  and  Preiss  (9)  examined  155  normal  Volkschule  chil- 
dren (79  boys  and  76  girls)  varying  in  age  from  7  to  13.  Bober- 
tag's  translation  was  used.  These  investigators  found  very  strik- 
ing differences  in  the  reaction  of  the  sexes  to  the  individual  tests, 
the  differences  running  as  high  as  52%,  most  of  them  in  favor 
of  the  boys.  The  differences  between  the  performances  of  the 
boys  and  girls  of  each  age  were  calculated,  without  reference  to 
the  many  sources  of  variation.  The  factor  of  the  personal  equa- 
tion is  not  treated,  and  this  factor  alone  might  cause  these  varia- 
tions. If  a  more  careful  analysis  of  the  results  had  been 
made,  it  is  very  probable  that  the  conclusions  would  have 
been  modified  to  some  extent.      The    fact    that    the    11    year 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  87 

boys  are  37%  higher  than  the  11  year  girls  on  the  test 
of  criticising  absurdities  is  most  certainly  modified  by  the 
fact  that  the  11  year  subjects  are  30%  lower  than  the  10 
year  subjects  in  the  test  of  repeating  7  digits.  The  small  num- 
ber of  subjects  (in  five  cases  less  than  10),  would  tend  to  empha- 
size chance  variations.  The  fact  that  the  number  of  subjects  is 
too  small  to  warrant  definite  conclusions  is  pointed  out  by  the 
authors.  Stern  (62)  in  commenting  upon  these  results,  points 
out  the  significance  of  the  fact  that  the  inferiority  of  the  girls 
extends  to  so  many  different  kinds  of  tests.  The  results  of 
Bloch  and  Preiss  are  in  almost  complete  contradiction  to  the  re- 
sults of  the  present  investigation.  They  find  large  differences, 
and  find  practically  all  of  these  differences  in  favor  of  the  boys. 
This  investigation  shows  a  general  run  of  differences  very  much 
smaller,  and  a  slight  general  superiority  of  the  non-selected  girls. 
The  mere  fact  of  contradiction  in  the  results  of  the  two  investiga- 
tions would  indicate  that  the  differences  were  not  produced  by 
the  common  factor  of  sex.  Rogers  and  Mclntyre  (54)  give  no 
figures,  but  report  that  they  have  studied  their  results  in  the  light 
of  sex  differences,  and  have  found  no  correlation  between  their 
results  and  those  of  Bloch  and  Preiss. 

The  results  of  the  investigators  who  have  compared  the  "men- 
tal ages"  or  total  scores  of  children  of  different  sexes  are  some- 
what at  variance.  Goddard  (30)  reports  that  there  are  more 
backward  boys  than  girls.  Stern  notes  that  Goddard's  results 
do  not  bear  out  his  statement,  for  the  percentage  of  boys  and 
girls  testing  two  or  more  years  retarded  is  the  same  (18.5%). 
The  accuracy  of  Goddard's  statement  depends  on  the  criterion** 
used  for  measuring  backwardness.     Although  Goddard's  state- 

^  If  the  criterion  is  four  or  more  years  retarded,  there  are  more  backward 
boys  than  girls  (boys  =  3-7%,  girls  =  3.1%).  If  the  criterion  is  three  or 
more  years  backward,  there  are  more  girls  than  boys  (boys  =  8%, 
girls  =  9.1%).  If  the  criterion  is  two  or  more  years  backward,  the  propor- 
tions are  the  same,  as  Stern  notes.  If  the  criterion  is  one  year  or  more  re- 
tarded, there  are  more  backward  boys  than  girls  (boys  =  41.4%,  girls  = 
35-6%).  There  are  more  girls  than  boys  testing  at  and  above  age  according 
to  Goddard's  results.  34.7%  of  the  boys  and  36.6%  of  the  girls  test  at  age, 
while  23.8%  of  the  boys  and  27.7%  of  the  girls  test  one  year  or  more  above 
age. 


88  CARL  C.  B  RICH  AM 

ment  concerning  the  backwardness  of  the  boys  may  be  interpreted 
differently,  his  figures  leave  no  doubt  concerning  the  fact  that 
there  are  more  girls  than  boys  at  and  above  age,  and  therefore 
indicate  a  general  superiority  of  the  girls. 

Bobertag  (lo)  computed  the  average  "mental  age"  of  90  boys 
and  90  girls  regularly  distributed  from  7  to  12.  The  subjects 
were  selected  according  to  school  grades,  so  that  the  average 
grade  of  each  group  differed  by  exactly  one  grade.  His  results 
show  the  boys  ahead  0.06  yr.  at  7,  0.14  yr.  at  8  and  9,  0.20  yr. 
at  10,  0.19  yr.  at  11  and  0.14  yr.  at  12.  These  findings  cannot 
be  considered  entirely  out  of  harmony  with  those  of  Goddard, 
for,  as  this  investigation  shows,  there  may  be  a  change  in  the 
relation  of  non-selected  boys  and  girls  and  selected  boys  and  girls. 

Yerkes  and  his  co-workers  (82),  scoring  some  of  the  Binet 
tests  according  to  the  point  system,  show  that  the  girls  of  English 
speaking  parents  are  superior  to  the  boys  of  the  same  parentage 
between  5  and  7,  that  they  fall  below  with  minor  variations  till 
II,  where  they  again  surpass  the  boys  at  12  and  13,  falling  below 
at  14  and  15.  The  differences  between  the  sexes  are  smaller 
and  of  less  practical  importance  than  the  differences  due  to  the 
language  factor,  but  the  authors  suspect  "that  at  certain  ages 
serious  injustice  will  be  done  to  individuals  by  evaluating  their 
scores  in  the  light  of  norms  which  do  not  take  account  of  sex 
differences."  (page  73).  In  contradiction  to  these  results  are 
those  of  Terman  and  his  co-workers  (67),  who,  scoring  the 
Stanford  revision  of  the  Binet  scale  according  to  "intelligence 
quotients,"  find  differences  of  but  2%  to  4%  in  these  quotients 
in  favor  of  the  girls,  and  who  conclude  from  the  basis  of  their 
studies  of  sex  differences  that  the  conclusions  of  Yerkes  are 
unjustified.  These  two  investigations  used  tests  different  in 
character  and  differently  weighted,  so  that  the  results  would  not 
necessarily  have  to  correspond. 

The  one  common  feature  of  most  of  the  researches  on  sex 
differences  in  the  Binet-Simon  tests  is  that  the  differences  are 
small.  Burt  and  Moore  (17)  summarize  the  work  of  various  in- 
vestigators in  the  general  field  of  sex  differences,  and  report  an 
investigation  of  their  own  on  67  boys  and  62,  girls,  125^  to  13^ 


VARIABLE  FACTORS  IN  THE  BINET  TESTS  85 

years  of  age.  They  discuss  their  results  and  those  of  the  other 
authors  in  the  order  of  the  complexity  of  the  mental  processes 
involved.  They  find  a  high  correlation  between  the  size  of  the 
sex  difference  and  the  simplicity  of  the  capacities  compared — the 
higher  the  process,  and  the  more  complex  the  capacity,  the 
smaller  the  sex  difference. 

The  general  trend  of  the  investigations  on  sex  differences  indi- 
cates that  no  very  large  differences  are  to  be  expected  in  the 
application  of  intelligence  tests,  and  that  the  differences  to  be 
expected  will  vary  according  to  the  nature  of  the  tests.  The  re- 
sults of  this  investigation  are  in  agreement  with  the  general 
trend  of  the  investigations  in  showing  only  slight  differences  that 
might  be  attributed  to  the  sex  factor.  The  results  do  not  show 
on  what  tests,  if  any,  these  differences  occur.  Conclusions  con- 
cerning the  amount  of  influence  of  this  factor  must  be  drawn 
from  more  exhaustive  investigations  on  the  individual  tests.  The 
research  of  Bateman  (3),  for  instance,  is  conclusive  in  the  test 
of  naming  colors.  Bateman  shows  that  there  is  a  difference  of 
14%  in  favor  of  the  girls  in  this  test,  showing  furthermore  that 
the  factor  of  school  training  causes  an  improvement  of  but  18%. 
The  results  would  indicate  that  the  test  should  be  placed  in  the 
fifth  or  sixth  year,  but  the  sex  difference  of  14%  would  probably 
not  warrant  the  placing  of  the  test  in  a  different  age  group  for 
boys  and  girls. 

The  investigations  of  Bolton  (11)  and  Wooley  (79)  would 
show  that  small  differences  in  favor  of  the  girls  are  to  be  ex- 
pected in  the  tests  of  repeating  digits,  and  possibly  in  all  memory 
tests.  The  investigations  of  Gilbert  (27),  Thompson  (68), 
Burt  and  Moore,  and  Peterson  and  Doll  (51)  would  indicate  that 
a  slight  difference  in  favor  of  the  boys  should  appear  in  the  test 
of  arranging  five  weights.  Ruger's  (55)  finding  of  striking  dif- 
ferences in  favor  of  men  in  a  series  of  puzzle  tests,  and  Wooley 
and  Fisher's  finding  of  large  differences  in  favor  of  the  boys  in 
the  Healy  puzzle-box  test  would  show  that  rather  large  differ- 
ences might  appear  in  the  general  class  of  "puzzle"  tests. 

Even  though  the  sex  differences  in  intelligence  tests  may  be 
shown  to  be  small,  scientific  procedure  should  demand  that  the 


90  CARL  C.  BRIGHAM 

investigator  who  standardizes  any  test  or  system  of  tests  should 
treat  his  results  in  such  a  way  as  to  demonstrate  that  the  factor 
is  present  or  not  present.  The  burden  of  proof  should  still  be 
on  the  person  who  maintains  that  sex  differences  are  not  involved. 
The  knowledge  of  sex  differences  is  especially  important  in  diag- 
nosing border-line  cases  of  mental  defect,  where  the  diagnosis 
must  often  be  made  on  the  qualitatively  different  character  of 
the  responses  to  individual  tests. 


4 


VI.     SUMMARY. 

One  of  the  fundamental  assumptions  in  the  construction  of  the 
Binet-Simon  scale  is  the  correlation  of  the  individual  tests  with 
age.  The  correlation  of  the  tests  with  age  is  affected  by  the 
error  due  to  incomplete  data,  by  the  influence  of  the  personal 
equation  of  the  experimenter,  and  by  the  training  the  subject  has 
received  in  school. 

The  influence  of  the  personal  equation  of  the  experimenter  was 
found  to  be  more  marked  in  some  tests  than  in  others,  the  in- 
fluence being  most  marked  in  the  tests  of  copying  the  diamond, 
indicating  omissions  in  pictures,  defining  in  terms  superior  to 
use,  drawing  designs  from  memory,  detecting  absurdities  in  state- 
ments and  reconstructing  dissected  sentences. 

The  variations  between  the  experimenters  could  be  traced  to 
three  sources, — 

1 )  to  the  use  of  apparatus,  variations  in  which  were  due  to, 

a)  the  construction  of  the  test  material,  and 

b)  the  use  of  alternative  questions; 

2)  to  the  technique  of  the  experimenters  in  giving  the  tests; 
and 

3)  to  observation  errors  made  by  the  experimenters  in  mark- 
ing a  response  passed  or  failed. 

It  is  possible  to  eliminate  all  three  sources  of  error. 

The  effect  of  school  training  was  more  marked  on  some  tests 
than  on  others,  the  eft'ect  being  most  marked  in  the  tests  of  count- 
ing stamps,  counting  backward  from  20  to  o.  enumerating  the 
days  of  the  week  and  the  months,  giving  the  day  and  the  date, 
naming  the  pieces  of  money,  making  change,  and  reconstructing 
dissected  sentences.  Tests  that  involve  school  training  should  be 
standardized  on  a  different  basis  than  those  relatively  independent 
of  this  factor. 

Although  the  comparison  of  "mental  ages"  and  pedagogical 
ages  gives  no  information  concerning  the  general  correlation  be- 


92  CARL  C.  BRIG  HAM 

tween  the  Binet  tests  and  the  school  grades,  the  study  of  the 
individual  tests  establishes  the  fact  of  a  general  correlation. 

The  correlation  of  the  individual  tests  with  grade  is  higher  m 

than  the  correlation  of  the  tests  with  age,  this  fact  being  indirect  | 

evidence  of  the  value  of  the  tests  as  measures  of  intelligence.  t 

Sex  differences  were  found  to  be  slight  as  compared  with  the  | 

influence  due  to  the  personal  equation  or  grade  training.  I 

Since  variations  occur  in  the  results  due  to  the  influence  of  the 
personal  equation  and  grade  training,  certain  allowances  must 
be  made  for  these  factors  in  making  diagnoses  on  the  basis  of 
the  tests.  The  scale  is  therefore  a  qualitative  rather  than  a  quan- 
titative instrument. 

The  investigator  who  wishes  to  use  his  results  for  standard- 
izing age  norms  should  use  only  those  data  based  on  the  com- 
plete method  of  experimenting,  and  should  treat  his  results  in 
such  a  way  as  to  demonstrate  the  presence  or  absence  of  the 
variable  factors  of  the  personal  equation,  grade  training  and  sex 
differences. 


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